class4_and_5_6110T.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Defaulting to user installation because normal site-packages is not writeable\n",
      "Requirement already satisfied: scipy in /Users/delinaivanova/Library/Python/3.9/lib/python/site-packages (1.13.0)\n",
      "Requirement already satisfied: numpy<2.3,>=1.22.4 in /Users/delinaivanova/Library/Python/3.9/lib/python/site-packages (from scipy) (1.26.4)\n",
      "\u001b[33mWARNING: You are using pip version 21.2.4; however, version 24.0 is available.\n",
      "You should consider upgrading via the '/Applications/Xcode.app/Contents/Developer/usr/bin/python3 -m pip install --upgrade pip' command.\u001b[0m\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.random.normal(loc=50, scale=10, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.,  0.,  2.,  1.,  0.,  0.,  1.,  3.,  6.,  6.,  5., 10.,  6.,\n",
       "        15., 16., 18., 26., 30., 31., 24., 29., 45., 29., 57., 58., 44.,\n",
       "        66., 52., 56., 52., 47., 34., 40., 30., 28., 20., 16., 16., 12.,\n",
       "        18., 14.,  9., 11.,  4.,  3.,  2.,  4.,  0.,  1.,  1.]),\n",
       " array([17.82654885, 19.05644276, 20.28633668, 21.51623059, 22.74612451,\n",
       "        23.97601842, 25.20591233, 26.43580625, 27.66570016, 28.89559407,\n",
       "        30.12548799, 31.3553819 , 32.58527581, 33.81516973, 35.04506364,\n",
       "        36.27495755, 37.50485147, 38.73474538, 39.96463929, 41.19453321,\n",
       "        42.42442712, 43.65432103, 44.88421495, 46.11410886, 47.34400277,\n",
       "        48.57389669, 49.8037906 , 51.03368451, 52.26357843, 53.49347234,\n",
       "        54.72336625, 55.95326017, 57.18315408, 58.41304799, 59.64294191,\n",
       "        60.87283582, 62.10272973, 63.33262365, 64.56251756, 65.79241147,\n",
       "        67.02230539, 68.2521993 , 69.48209321, 70.71198713, 71.94188104,\n",
       "        73.17177495, 74.40166887, 75.63156278, 76.86145669, 78.09135061,\n",
       "        79.32124452]),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data, bins=50, alpha=0.7, color='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(data, dist='norm', plot=plt);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.051130677461654506\n",
      "0.10206064550181004\n"
     ]
    }
   ],
   "source": [
    "print(stats.skew(data))\n",
    "print(stats.kurtosis(data, fisher=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# poisson distribution\n",
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mqaeeUnt7u/Ly8tTS0qI777xT5eXlioyMDHY5AABgDAh6YImOjtaGDRu0YcOGXts4HA6tWbNGa9asCfbbAwCAMYhnCQEAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwXuhIF4DxK3tH9kiXAAAYJbjCAgAArEdgAQAA1huSwPLJJ5/oa1/7mhISEhQVFaXp06fryJEjvu3GGK1atUrJycmKioqS2+3WiRMnhqIUAAAwBgQ9sPzf//2f7rjjDoWFhenXv/61fv/73+tHP/qRrrnmGl+bdevWaePGjSotLVV1dbUmTJigzMxMdXR0BLscAAAwBgT9ptu1a9cqJSVFW7Zs8a1LS0vz/dsYow0bNuiZZ57RggULJEmvvfaakpKStHv3bi1atCjYJQEAgFEu6FdY3n77bc2aNUtf/epXlZiYqFtuuUW/+MUvfNvr6+vl8Xjkdrt962JjY5Wenq6qqqoe++zs7JTX6/VbAADA+BH0wPLf//3f2rx5syZPnqx3331Xjz76qB5//HG9+uqrkiSPxyNJSkpK8tsvKSnJt+1SxcXFio2N9S0pKSnBLhsAAFgs6IGlu7tbt956q77//e/rlltuUV5enpYtW6bS0tJB91lUVKTW1lbf0tDQEMSKAQCA7YIeWJKTk/XFL37Rb920adN0+vRpSZLT6ZQkNTU1+bVpamrybbtURESEYmJi/BYAADB+BD2w3HHHHaqrq/Nb94c//EETJ06U9LcbcJ1OpyorK33bvV6vqqurlZGREexyAADAGBD0bwk98cQTuv322/X9739fDzzwgA4dOqSf//zn+vnPfy5JcjgcWr58uV544QVNnjxZaWlpWrlypVwulxYuXBjscgAAwBgQ9MBy2223adeuXSoqKtKaNWuUlpamDRs2KDc319fmqaeeUnt7u/Ly8tTS0qI777xT5eXlioyMDHY5AABgDBiShx9++ctf1pe//OVetzscDq1Zs0Zr1qwZircHAABjDM8SAgAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWG5JfugWA8SZ7R/ag9y1bXBbESoCxiSssAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWG/LA8oMf/EAOh0PLly/3revo6FB+fr4SEhJ09dVXKycnR01NTUNdCgAAGKWGNLAcPnxYL730km666Sa/9U888YTKysq0c+dO7d+/X42Njbr//vuHshQAADCKDVlgaWtrU25urn7xi1/ommuu8a1vbW3Vyy+/rBdffFF33323Zs6cqS1btuiDDz7QwYMHh6ocAAAwig1ZYMnPz9f8+fPldrv91tfU1Kirq8tv/dSpU5Wamqqqqqoe++rs7JTX6/VbAADA+BE6FJ2+/vrrqq2t1eHDhy/b5vF4FB4erri4OL/1SUlJ8ng8PfZXXFys5557bihKBQAAo0DQr7A0NDToO9/5jrZt26bIyMig9FlUVKTW1lbf0tDQEJR+AQDA6BD0wFJTU6Pm5mbdeuutCg0NVWhoqPbv36+NGzcqNDRUSUlJOn/+vFpaWvz2a2pqktPp7LHPiIgIxcTE+C0AAGD8CPqfhObOnauPPvrIb90jjzyiqVOnasWKFUpJSVFYWJgqKyuVk5MjSaqrq9Pp06eVkZER7HIAAMAYEPTAEh0drRtvvNFv3YQJE5SQkOBbv3TpUhUWFio+Pl4xMTF67LHHlJGRoS996UvBLgcAAIwBQ3LTbX9+/OMfKyQkRDk5Oers7FRmZqZ+9rOfjUQpkJS9I3vQ+5YtLgtiJQAA9GxYAsu+ffv8XkdGRqqkpEQlJSXD8fYAAGCU41lCAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsF7oSBcAAONd9o7sQe9btrgsiJUA9uIKCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYLemApLi7WbbfdpujoaCUmJmrhwoWqq6vza9PR0aH8/HwlJCTo6quvVk5OjpqamoJdCgAAGCOCHlj279+v/Px8HTx4UBUVFerq6tI999yj9vZ2X5snnnhCZWVl2rlzp/bv36/Gxkbdf//9wS4FAACMEaHB7rC8vNzv9datW5WYmKiamhr98z//s1pbW/Xyyy9r+/btuvvuuyVJW7Zs0bRp03Tw4EF96UtfCnZJAABglBvye1haW1slSfHx8ZKkmpoadXV1ye12+9pMnTpVqampqqqq6rGPzs5Oeb1evwUAAIwfQxpYuru7tXz5ct1xxx268cYbJUkej0fh4eGKi4vza5uUlCSPx9NjP8XFxYqNjfUtKSkpQ1k2AACwzJAGlvz8fH388cd6/fXXr6ifoqIitba2+paGhoYgVQgAAEaDoN/DclFBQYH27NmjAwcO6LrrrvOtdzqdOn/+vFpaWvyusjQ1NcnpdPbYV0REhCIiIoaqVAAAYLmgX2ExxqigoEC7du3S3r17lZaW5rd95syZCgsLU2VlpW9dXV2dTp8+rYyMjGCXAwAAxoCgX2HJz8/X9u3b9dZbbyk6Otp3X0psbKyioqIUGxurpUuXqrCwUPHx8YqJidFjjz2mjIwMviEEAAB6FPTAsnnzZknSnDlz/NZv2bJFDz/8sCTpxz/+sUJCQpSTk6POzk5lZmbqZz/7WbBLGVeyd2SPdAkARpkr+e9G2eKyIFYC9C/ogcUY02+byMhIlZSUqKSkJNhvDwAAxiCeJQQAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6oSNdwFiTvSN70PuWLS4LYiUAAIwdXGEBAADWI7AAAADrEVgAAID1CCwAAMB63HQLAAgYXzDAcOMKCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6/EtoR5cyd3vAAAg+LjCAgAArEdgAQAA1iOwAAAA6xFYAACA9bjpFgAwaozUlyJ4nMDI4woLAACwHoEFAABYb0QDS0lJiSZNmqTIyEilp6fr0KFDI1kOAACw1IgFll/96lcqLCzU6tWrVVtbqxkzZigzM1PNzc0jVRIAALDUiN10++KLL2rZsmV65JFHJEmlpaV655139Morr+jpp58eqbIAAAiq0frr6bbdaDwigeX8+fOqqalRUVGRb11ISIjcbreqqqoua9/Z2anOzk7f69bWVkmS1+sdkvq6znUNSb/9uZLxUPPAUfPwoObhQc3DYzTWfKWG4hx7sU9jTOA7mxHwySefGEnmgw8+8Fv/5JNPmtmzZ1/WfvXq1UYSCwsLCwsLyxhYGhoaAs4Oo+J3WIqKilRYWOh73d3drTNnzighIUEOh2PE6vJ6vUpJSVFDQ4NiYmJGrI6hMtbHJ439MTK+0W+sj5HxjX6BjNEYo7Nnz8rlcgX8PiMSWK699lpdddVVampq8lvf1NQkp9N5WfuIiAhFRET4rYuLixvKEgMSExMzZg9EaeyPTxr7Y2R8o99YHyPjG/0GOsbY2NhB9T8i3xIKDw/XzJkzVVlZ6VvX3d2tyspKZWRkjERJAADAYiP2J6HCwkItWbJEs2bN0uzZs7Vhwwa1t7f7vjUEAABw0YgFlgcffFD/+7//q1WrVsnj8ejmm29WeXm5kpKSRqqkgEVERGj16tWX/blqrBjr45PG/hgZ3+g31sfI+Ea/4Rqjw5jBfLcIAABg+PAsIQAAYD0CCwAAsB6BBQAAWI/AAgAArEdg6UVxcbFuu+02RUdHKzExUQsXLlRdXV2f+2zdulUOh8NviYyMHKaKA/Pss89eVuvUqVP73Gfnzp2aOnWqIiMjNX36dP3Hf/zHMFU7OJMmTbpsjA6HQ/n5+T22t33+Dhw4oOzsbLlcLjkcDu3evdtvuzFGq1atUnJysqKiouR2u3XixIl++y0pKdGkSZMUGRmp9PR0HTp0aIhG0L++xtjV1aUVK1Zo+vTpmjBhglwul77+9a+rsbGxzz4Hc6wPlf7m8OGHH76s1nnz5vXbry1z2N/4evo8OhwO/fCHP+y1T5vmbyDnhY6ODuXn5yshIUFXX321cnJyLvuR1EsN9rM7FPob45kzZ/TYY49pypQpioqKUmpqqh5//HHfM/56M9hj++8RWHqxf/9+5efn6+DBg6qoqFBXV5fuuecetbe397lfTEyMPv30U99y6tSpYao4cDfccINfrb/97W97bfvBBx9o8eLFWrp0qY4ePaqFCxdq4cKF+vjjj4ex4sAcPnzYb3wVFRWSpK9+9au97mPz/LW3t2vGjBkqKSnpcfu6deu0ceNGlZaWqrq6WhMmTFBmZqY6Ojp67fNXv/qVCgsLtXr1atXW1mrGjBnKzMxUc3PzUA2jT32N8dy5c6qtrdXKlStVW1urN998U3V1dbrvvvv67TeQY30o9TeHkjRv3jy/Wnfs2NFnnzbNYX/j+/txffrpp3rllVfkcDiUk5PTZ7+2zN9AzgtPPPGEysrKtHPnTu3fv1+NjY26//77++x3MJ/dodLfGBsbG9XY2Kj169fr448/1tatW1VeXq6lS5f223egx/ZlBvPwwvGoubnZSDL79+/vtc2WLVtMbGzs8BV1BVavXm1mzJgx4PYPPPCAmT9/vt+69PR0881vfjPIlQ2d73znO+b666833d3dPW4fTfMnyezatcv3uru72zidTvPDH/7Qt66lpcVERESYHTt29NrP7NmzTX5+vu/1hQsXjMvlMsXFxUNSdyAuHWNPDh06ZCSZU6dO9dom0GN9uPQ0viVLlpgFCxYE1I+tcziQ+VuwYIG5++67+2xj6/wZc/l5oaWlxYSFhZmdO3f62hw/ftxIMlVVVT32MdjP7nAZyLnvjTfeMOHh4aarq6vXNoM5ti/FFZYBuni5Kz4+vs92bW1tmjhxolJSUrRgwQIdO3ZsOMoblBMnTsjlcunzn/+8cnNzdfr06V7bVlVVye12+63LzMxUVVXVUJcZFOfPn9cvf/lLfeMb3+jzgZmjaf7+Xn19vTwej98cxcbGKj09vdc5On/+vGpqavz2CQkJkdvtHjXz2traKofD0e+zxQI51kfavn37lJiYqClTpujRRx/VX/7yl17bjuY5bGpq0jvvvDOg/zO3df4uPS/U1NSoq6vLbz6mTp2q1NTUXudjMJ/d4TSQc19ra6tiYmIUGtr3b9EGcmz3hMAyAN3d3Vq+fLnuuOMO3Xjjjb22mzJlil555RW99dZb+uUvf6nu7m7dfvvt+tOf/jSM1Q5Menq671Le5s2bVV9fr3/6p3/S2bNne2zv8Xgu+xXipKQkeTye4Sj3iu3evVstLS16+OGHe20zmubvUhfnIZA5+vOf/6wLFy6M2nnt6OjQihUrtHjx4j4fuBbosT6S5s2bp9dee02VlZVau3at9u/fr6ysLF24cKHH9qN5Dl999VVFR0f3++cSW+evp/OCx+NReHj4ZQG6r/kYzGd3uAzk3PfnP/9Zzz//vPLy8vrsK9Bjuycj9tP8o0l+fr4+/vjjfv9umpGR4ffwxttvv13Tpk3TSy+9pOeff36oywxIVlaW79833XST0tPTNXHiRL3xxhsD+j+e0ebll19WVlZWn480H03zN951dXXpgQcekDFGmzdv7rPtaDrWFy1a5Pv39OnTddNNN+n666/Xvn37NHfu3BGsLPheeeUV5ebm9ntju63zN9DzwmjW3xi9Xq/mz5+vL37xi3r22Wf77CsYxzZXWPpRUFCgPXv26P3339d1110X0L5hYWG65ZZbdPLkySGqLnji4uL0hS98oddanU7nZXe6NzU1yel0Dkd5V+TUqVN677339G//9m8B7Tea5u/iPAQyR9dee62uuuqqUTevF8PKqVOnVFFRMaDH2f+9/o51m3z+85/Xtdde22uto3UOf/Ob36iuri7gz6Rkx/z1dl5wOp06f/68Wlpa/Nr3NR+D+ewOh/7OfWfPntW8efMUHR2tXbt2KSwsLKD++zu2e0Jg6YUxRgUFBdq1a5f27t2rtLS0gPu4cOGCPvroIyUnJw9BhcHV1tamP/7xj73WmpGRocrKSr91FRUVflckbLVlyxYlJiZq/vz5Ae03muYvLS1NTqfTb468Xq+qq6t7naPw8HDNnDnTb5/u7m5VVlZaO68Xw8qJEyf03nvvKSEhIeA++jvWbfKnP/1Jf/nLX3qtdTTOofS3K54zZ87UjBkzAt53JOevv/PCzJkzFRYW5jcfdXV1On36dK/zMZjP7lAayLnP6/XqnnvuUXh4uN5+++1B/fxDf8d2b8WhB48++qiJjY01+/btM59++qlvOXfunK/NQw89ZJ5++mnf6+eee868++675o9//KOpqakxixYtMpGRkebYsWMjMYQ+ffe73zX79u0z9fX15ne/+51xu93m2muvNc3NzcaYy8f2u9/9zoSGhpr169eb48ePm9WrV5uwsDDz0UcfjdQQBuTChQsmNTXVrFix4rJto23+zp49a44ePWqOHj1qJJkXX3zRHD161PcNmR/84AcmLi7OvPXWW+a//uu/zIIFC0xaWpr561//6uvj7rvvNps2bfK9fv31101ERITZunWr+f3vf2/y8vJMXFyc8Xg8wz4+Y/oe4/nz5819991nrrvuOvPhhx/6fS47Ozt9fVw6xv6OdVvGd/bsWfPv//7vpqqqytTX15v33nvP3HrrrWby5Mmmo6Oj1/HZNIf9HaPGGNPa2mo+97nPmc2bN/fYh83zN5Dzwre+9S2Tmppq9u7da44cOWIyMjJMRkaGXz9Tpkwxb775pu/1QD67w6W/Mba2tpr09HQzffp0c/LkSb82n332WY9jHOix3R8CSy8k9bhs2bLF1+Zf/uVfzJIlS3yvly9fblJTU014eLhJSkoy9957r6mtrR3+4gfgwQcfNMnJySY8PNz84z/+o3nwwQfNyZMnfdsvHZsxf/vq2he+8AUTHh5ubrjhBvPOO+8Mc9WBe/fdd40kU1dXd9m20TZ/77//fo/H5MUxdHd3m5UrV5qkpCQTERFh5s6de9m4J06caFavXu23btOmTb5xz5492xw8eHCYRnS5vsZYX1/f6+fy/fff9/Vx6Rj7O9aHU1/jO3funLnnnnvMP/zDP5iwsDAzceJEs2zZssuCh81z2N8xaowxL730komKijItLS099mHz/A3kvPDXv/7VfPvb3zbXXHON+dznPme+8pWvmE8//fSyfv5+n4F8dodLf2PsbY4lmfr6er9+Lu4z0GO7P47/3zEAAIC1uIcFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOv9P9rFt5209EjpAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = poisson.rvs(mu=10, size=1000)\n",
    "\n",
    "plt.hist(data, bins=30, alpha=0.7, color='green');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# exponential distribution\n",
    "data = np.random.exponential(scale=30, size=1000)\n",
    "\n",
    "plt.hist(data, bins=50, color='red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((array([6.93147181e-04, 1.68330207e-03, 2.68512296e-03, 3.68794851e-03,\n",
       "         4.69178072e-03, 5.69662163e-03, 6.70247325e-03, 7.70933763e-03,\n",
       "         8.71721682e-03, 9.72611284e-03, 1.07360278e-02, 1.17469636e-02,\n",
       "         1.27589226e-02, 1.37719066e-02, 1.47859178e-02, 1.58009582e-02,\n",
       "         1.68170300e-02, 1.78341353e-02, 1.88522761e-02, 1.98714545e-02,\n",
       "         2.08916728e-02, 2.19129330e-02, 2.29352372e-02, 2.39585876e-02,\n",
       "         2.49829863e-02, 2.60084354e-02, 2.70349372e-02, 2.80624938e-02,\n",
       "         2.90911074e-02, 3.01207801e-02, 3.11515141e-02, 3.21833116e-02,\n",
       "         3.32161748e-02, 3.42501059e-02, 3.52851071e-02, 3.63211807e-02,\n",
       "         3.73583289e-02, 3.83965538e-02, 3.94358578e-02, 4.04762430e-02,\n",
       "         4.15177118e-02, 4.25602664e-02, 4.36039090e-02, 4.46486419e-02,\n",
       "         4.56944675e-02, 4.67413879e-02, 4.77894056e-02, 4.88385227e-02,\n",
       "         4.98887416e-02, 5.09400647e-02, 5.19924942e-02, 5.30460325e-02,\n",
       "         5.41006818e-02, 5.51564447e-02, 5.62133233e-02, 5.72713202e-02,\n",
       "         5.83304376e-02, 5.93906779e-02, 6.04520435e-02, 6.15145367e-02,\n",
       "         6.25781601e-02, 6.36429160e-02, 6.47088068e-02, 6.57758350e-02,\n",
       "         6.68440029e-02, 6.79133130e-02, 6.89837677e-02, 7.00553696e-02,\n",
       "         7.11281210e-02, 7.22020244e-02, 7.32770824e-02, 7.43532973e-02,\n",
       "         7.54306718e-02, 7.65092082e-02, 7.75889091e-02, 7.86697770e-02,\n",
       "         7.97518145e-02, 8.08350241e-02, 8.19194082e-02, 8.30049695e-02,\n",
       "         8.40917106e-02, 8.51796339e-02, 8.62687422e-02, 8.73590378e-02,\n",
       "         8.84505235e-02, 8.95432019e-02, 9.06370755e-02, 9.17321469e-02,\n",
       "         9.28284189e-02, 9.39258940e-02, 9.50245749e-02, 9.61244642e-02,\n",
       "         9.72255645e-02, 9.83278787e-02, 9.94314093e-02, 1.00536159e-01,\n",
       "         1.01642130e-01, 1.02749327e-01, 1.03857750e-01, 1.04967403e-01,\n",
       "         1.06078289e-01, 1.07190410e-01, 1.08303770e-01, 1.09418371e-01,\n",
       "         1.10534215e-01, 1.11651306e-01, 1.12769646e-01, 1.13889238e-01,\n",
       "         1.15010085e-01, 1.16132190e-01, 1.17255555e-01, 1.18380184e-01,\n",
       "         1.19506078e-01, 1.20633242e-01, 1.21761678e-01, 1.22891389e-01,\n",
       "         1.24022377e-01, 1.25154646e-01, 1.26288199e-01, 1.27423037e-01,\n",
       "         1.28559165e-01, 1.29696586e-01, 1.30835301e-01, 1.31975315e-01,\n",
       "         1.33116630e-01, 1.34259249e-01, 1.35403175e-01, 1.36548411e-01,\n",
       "         1.37694960e-01, 1.38842826e-01, 1.39992010e-01, 1.41142516e-01,\n",
       "         1.42294348e-01, 1.43447508e-01, 1.44601999e-01, 1.45757825e-01,\n",
       "         1.46914988e-01, 1.48073492e-01, 1.49233339e-01, 1.50394533e-01,\n",
       "         1.51557077e-01, 1.52720975e-01, 1.53886228e-01, 1.55052841e-01,\n",
       "         1.56220816e-01, 1.57390157e-01, 1.58560868e-01, 1.59732950e-01,\n",
       "         1.60906408e-01, 1.62081244e-01, 1.63257462e-01, 1.64435065e-01,\n",
       "         1.65614057e-01, 1.66794440e-01, 1.67976219e-01, 1.69159395e-01,\n",
       "         1.70343973e-01, 1.71529956e-01, 1.72717348e-01, 1.73906150e-01,\n",
       "         1.75096368e-01, 1.76288004e-01, 1.77481062e-01, 1.78675545e-01,\n",
       "         1.79871456e-01, 1.81068799e-01, 1.82267578e-01, 1.83467795e-01,\n",
       "         1.84669455e-01, 1.85872560e-01, 1.87077115e-01, 1.88283122e-01,\n",
       "         1.89490586e-01, 1.90699509e-01, 1.91909895e-01, 1.93121749e-01,\n",
       "         1.94335072e-01, 1.95549870e-01, 1.96766145e-01, 1.97983901e-01,\n",
       "         1.99203142e-01, 2.00423872e-01, 2.01646093e-01, 2.02869810e-01,\n",
       "         2.04095026e-01, 2.05321746e-01, 2.06549972e-01, 2.07779708e-01,\n",
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       "         2.38978869e+00, 2.40075582e+00, 2.41184456e+00, 2.42305764e+00,\n",
       "         2.43439788e+00, 2.44586819e+00, 2.45747161e+00, 2.46921124e+00,\n",
       "         2.48109034e+00, 2.49311224e+00, 2.50528043e+00, 2.51759851e+00,\n",
       "         2.53007022e+00, 2.54269945e+00, 2.55549021e+00, 2.56844669e+00,\n",
       "         2.58157325e+00, 2.59487442e+00, 2.60835489e+00, 2.62201957e+00,\n",
       "         2.63587357e+00, 2.64992219e+00, 2.66417100e+00, 2.67862578e+00,\n",
       "         2.69329256e+00, 2.70817766e+00, 2.72328768e+00, 2.73862953e+00,\n",
       "         2.75421041e+00, 2.77003791e+00, 2.78611995e+00, 2.80246486e+00,\n",
       "         2.81908137e+00, 2.83597866e+00, 2.85316638e+00, 2.87065469e+00,\n",
       "         2.88845430e+00, 2.90657648e+00, 2.92503315e+00, 2.94383688e+00,\n",
       "         2.96300098e+00, 2.98253953e+00, 3.00246745e+00, 3.02280059e+00,\n",
       "         3.04355576e+00, 3.06475085e+00, 3.08640492e+00, 3.10853829e+00,\n",
       "         3.13117265e+00, 3.15433121e+00, 3.17803884e+00, 3.20232219e+00,\n",
       "         3.22720993e+00, 3.25273291e+00, 3.27892442e+00, 3.30582041e+00,\n",
       "         3.33345984e+00, 3.36188498e+00, 3.39114180e+00, 3.42128045e+00,\n",
       "         3.45235573e+00, 3.48442775e+00, 3.51756257e+00, 3.55183303e+00,\n",
       "         3.58731977e+00, 3.62411229e+00, 3.66231039e+00, 3.70202572e+00,\n",
       "         3.74338383e+00, 3.78652651e+00, 3.83161473e+00, 3.87883228e+00,\n",
       "         3.92839030e+00, 3.98053296e+00, 4.03554476e+00, 4.09375995e+00,\n",
       "         4.15557477e+00, 4.22146390e+00, 4.29200257e+00, 4.36789712e+00,\n",
       "         4.45002822e+00, 4.53951332e+00, 4.63780008e+00, 4.74681071e+00,\n",
       "         4.86917520e+00, 5.00862804e+00, 5.17072894e+00, 5.36428806e+00,\n",
       "         5.60452834e+00, 5.92137102e+00, 6.38783943e+00, 7.27461475e+00]),\n",
       "  array([4.96531331e-02, 6.18078715e-02, 7.40169962e-02, 8.50412611e-02,\n",
       "         1.16089689e-01, 1.24601113e-01, 1.43551752e-01, 1.62489674e-01,\n",
       "         1.96722472e-01, 2.46624590e-01, 2.74745682e-01, 2.95077915e-01,\n",
       "         3.16044699e-01, 3.19054904e-01, 3.24604010e-01, 3.75768209e-01,\n",
       "         4.09259386e-01, 4.13643106e-01, 4.23894414e-01, 4.48600192e-01,\n",
       "         4.63950684e-01, 5.04974961e-01, 5.48750589e-01, 5.61303173e-01,\n",
       "         5.77744237e-01, 6.14226305e-01, 6.25221500e-01, 6.25850327e-01,\n",
       "         6.51789439e-01, 6.89008825e-01, 7.80031881e-01, 7.95753665e-01,\n",
       "         8.47435298e-01, 8.66007002e-01, 9.19749137e-01, 9.21725352e-01,\n",
       "         9.50035720e-01, 9.54727844e-01, 9.54825796e-01, 9.66433510e-01,\n",
       "         9.70904734e-01, 9.71524352e-01, 9.99989720e-01, 1.01305605e+00,\n",
       "         1.07259818e+00, 1.09135372e+00, 1.11852654e+00, 1.12316259e+00,\n",
       "         1.12376808e+00, 1.14524397e+00, 1.15576846e+00, 1.20487209e+00,\n",
       "         1.20530969e+00, 1.20700983e+00, 1.28736953e+00, 1.38905288e+00,\n",
       "         1.39721920e+00, 1.40968272e+00, 1.41199177e+00, 1.41311952e+00,\n",
       "         1.43182410e+00, 1.47316824e+00, 1.48628346e+00, 1.50176100e+00,\n",
       "         1.50922815e+00, 1.55891404e+00, 1.56046480e+00, 1.56452013e+00,\n",
       "         1.56811018e+00, 1.58284764e+00, 1.59106606e+00, 1.59148930e+00,\n",
       "         1.65719937e+00, 1.66688763e+00, 1.75343978e+00, 1.75413006e+00,\n",
       "         1.75739988e+00, 1.78171402e+00, 1.79289134e+00, 1.84161130e+00,\n",
       "         1.86140667e+00, 1.86766766e+00, 1.87267906e+00, 1.88940665e+00,\n",
       "         1.89156115e+00, 1.89632644e+00, 1.92024480e+00, 1.93951395e+00,\n",
       "         1.97072038e+00, 1.99547729e+00, 1.99774016e+00, 2.00842709e+00,\n",
       "         2.01184041e+00, 2.08382859e+00, 2.13253868e+00, 2.16067038e+00,\n",
       "         2.17272461e+00, 2.22188820e+00, 2.22683860e+00, 2.24523764e+00,\n",
       "         2.26129847e+00, 2.29785003e+00, 2.39408411e+00, 2.41128861e+00,\n",
       "         2.47373582e+00, 2.48924767e+00, 2.54543786e+00, 2.54715465e+00,\n",
       "         2.55041433e+00, 2.55147170e+00, 2.56135806e+00, 2.60291017e+00,\n",
       "         2.64834990e+00, 2.66787407e+00, 2.67089466e+00, 2.67902226e+00,\n",
       "         2.68833431e+00, 2.69013480e+00, 2.79746849e+00, 2.80668481e+00,\n",
       "         2.81059102e+00, 2.84138234e+00, 2.86624485e+00, 2.93525947e+00,\n",
       "         2.97071826e+00, 3.01910374e+00, 3.09671005e+00, 3.09907828e+00,\n",
       "         3.13528602e+00, 3.15122983e+00, 3.19974349e+00, 3.21319750e+00,\n",
       "         3.34108091e+00, 3.43046665e+00, 3.43839347e+00, 3.45052942e+00,\n",
       "         3.46679514e+00, 3.51223848e+00, 3.52008129e+00, 3.60490486e+00,\n",
       "         3.65550007e+00, 3.66286303e+00, 3.74560662e+00, 3.75203711e+00,\n",
       "         3.75762779e+00, 3.78214087e+00, 3.81114266e+00, 3.85062037e+00,\n",
       "         3.87779239e+00, 3.88815915e+00, 3.89065365e+00, 3.95347638e+00,\n",
       "         4.00822570e+00, 4.02324911e+00, 4.03474187e+00, 4.04348188e+00,\n",
       "         4.08593084e+00, 4.17803629e+00, 4.25331879e+00, 4.34153948e+00,\n",
       "         4.37609125e+00, 4.43677307e+00, 4.48046347e+00, 4.52079033e+00,\n",
       "         4.60243502e+00, 4.60455413e+00, 4.74995355e+00, 4.83998656e+00,\n",
       "         4.87349257e+00, 4.89926301e+00, 4.90662649e+00, 4.93313480e+00,\n",
       "         5.04916462e+00, 5.04989026e+00, 5.07929785e+00, 5.11556790e+00,\n",
       "         5.16557478e+00, 5.18687092e+00, 5.23706788e+00, 5.25544868e+00,\n",
       "         5.26433405e+00, 5.27896499e+00, 5.33550688e+00, 5.37174922e+00,\n",
       "         5.41944962e+00, 5.43281160e+00, 5.46399736e+00, 5.52661656e+00,\n",
       "         5.54972393e+00, 5.57813095e+00, 5.58339466e+00, 5.59355911e+00,\n",
       "         5.65697704e+00, 5.70198614e+00, 5.71112121e+00, 5.74321155e+00,\n",
       "         5.74874513e+00, 5.78277323e+00, 5.80233782e+00, 5.80510322e+00,\n",
       "         5.82923966e+00, 5.83456372e+00, 5.87454663e+00, 5.91369343e+00,\n",
       "         5.96566562e+00, 5.99072887e+00, 6.04095562e+00, 6.14483226e+00,\n",
       "         6.16647670e+00, 6.19175041e+00, 6.20931710e+00, 6.25118537e+00,\n",
       "         6.26177811e+00, 6.28828833e+00, 6.33299123e+00, 6.33356197e+00,\n",
       "         6.37054056e+00, 6.37368627e+00, 6.42072206e+00, 6.42902923e+00,\n",
       "         6.53281601e+00, 6.53815598e+00, 6.62369948e+00, 6.84109479e+00,\n",
       "         6.90688675e+00, 6.90715683e+00, 7.07138918e+00, 7.08660026e+00,\n",
       "         7.13507161e+00, 7.27450917e+00, 7.31717337e+00, 7.31774043e+00,\n",
       "         7.34423097e+00, 7.39706400e+00, 7.46586999e+00, 7.47234041e+00,\n",
       "         7.51402110e+00, 7.56866426e+00, 7.73094317e+00, 7.86396047e+00,\n",
       "         7.88645968e+00, 7.89669605e+00, 7.96147374e+00, 7.98981380e+00,\n",
       "         8.21765359e+00, 8.22704251e+00, 8.29185071e+00, 8.35613741e+00,\n",
       "         8.38131902e+00, 8.38324920e+00, 8.44125939e+00, 8.49707829e+00,\n",
       "         8.50467224e+00, 8.51097280e+00, 8.57572707e+00, 8.62889283e+00,\n",
       "         8.63585717e+00, 8.71196029e+00, 8.74111976e+00, 8.79935744e+00,\n",
       "         8.80370893e+00, 8.87256436e+00, 8.89560884e+00, 8.94717304e+00,\n",
       "         9.00186694e+00, 9.00307739e+00, 9.05743719e+00, 9.05852720e+00,\n",
       "         9.14320687e+00, 9.14790767e+00, 9.16324839e+00, 9.19695519e+00,\n",
       "         9.21595037e+00, 9.23073471e+00, 9.28938002e+00, 9.32991074e+00,\n",
       "         9.35366444e+00, 9.39186424e+00, 9.42161191e+00, 9.49356903e+00,\n",
       "         9.51721400e+00, 9.53649581e+00, 9.54364273e+00, 9.68926197e+00,\n",
       "         9.69213887e+00, 9.75031151e+00, 9.91746682e+00, 9.91816439e+00,\n",
       "         9.98066828e+00, 1.00125986e+01, 1.00712133e+01, 1.01389911e+01,\n",
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       "         1.03874789e+01, 1.03981296e+01, 1.04126447e+01, 1.04299615e+01,\n",
       "         1.04443674e+01, 1.04457402e+01, 1.04663223e+01, 1.05664866e+01,\n",
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       "         1.11211203e+01, 1.11874362e+01, 1.13257877e+01, 1.13944893e+01,\n",
       "         1.14717140e+01, 1.14792969e+01, 1.14824568e+01, 1.15329290e+01,\n",
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       "         1.16602426e+01, 1.18103816e+01, 1.19314733e+01, 1.19539349e+01,\n",
       "         1.19545260e+01, 1.19776283e+01, 1.19853692e+01, 1.20550448e+01,\n",
       "         1.20635644e+01, 1.20776337e+01, 1.20964310e+01, 1.21169993e+01,\n",
       "         1.21173949e+01, 1.21344425e+01, 1.21532142e+01, 1.21926843e+01,\n",
       "         1.22223653e+01, 1.22276911e+01, 1.22299560e+01, 1.22721665e+01,\n",
       "         1.23182824e+01, 1.23944379e+01, 1.25268594e+01, 1.26025312e+01,\n",
       "         1.26668525e+01, 1.26880226e+01, 1.26953343e+01, 1.27130666e+01,\n",
       "         1.27539757e+01, 1.28031740e+01, 1.29028439e+01, 1.29686398e+01,\n",
       "         1.29988084e+01, 1.30534296e+01, 1.31068639e+01, 1.31493637e+01,\n",
       "         1.31898750e+01, 1.31923868e+01, 1.32110272e+01, 1.33552898e+01,\n",
       "         1.34293262e+01, 1.34325487e+01, 1.34555455e+01, 1.35023825e+01,\n",
       "         1.35101775e+01, 1.36526497e+01, 1.36831708e+01, 1.36832620e+01,\n",
       "         1.36888549e+01, 1.36929454e+01, 1.37041755e+01, 1.37456063e+01,\n",
       "         1.37564746e+01, 1.37650924e+01, 1.38152099e+01, 1.39665942e+01,\n",
       "         1.41070340e+01, 1.41279235e+01, 1.42415779e+01, 1.42913493e+01,\n",
       "         1.43882009e+01, 1.44248333e+01, 1.44287420e+01, 1.44921809e+01,\n",
       "         1.45039494e+01, 1.45348945e+01, 1.46451246e+01, 1.46586520e+01,\n",
       "         1.46909127e+01, 1.46932473e+01, 1.47193592e+01, 1.47663483e+01,\n",
       "         1.48444420e+01, 1.48599784e+01, 1.48935617e+01, 1.49220990e+01,\n",
       "         1.49711043e+01, 1.49794351e+01, 1.50312803e+01, 1.52435214e+01,\n",
       "         1.52491362e+01, 1.52534628e+01, 1.54058763e+01, 1.56387166e+01,\n",
       "         1.56450851e+01, 1.57855486e+01, 1.59437315e+01, 1.60145287e+01,\n",
       "         1.60405419e+01, 1.60670550e+01, 1.61246978e+01, 1.61316667e+01,\n",
       "         1.62160441e+01, 1.62653079e+01, 1.62788414e+01, 1.63758970e+01,\n",
       "         1.64341124e+01, 1.64913818e+01, 1.66224319e+01, 1.66625776e+01,\n",
       "         1.66721783e+01, 1.67498079e+01, 1.67634719e+01, 1.69324285e+01,\n",
       "         1.71698650e+01, 1.72439663e+01, 1.73083376e+01, 1.73842607e+01,\n",
       "         1.74008603e+01, 1.75179323e+01, 1.75667355e+01, 1.76432973e+01,\n",
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       "         1.77732480e+01, 1.77863396e+01, 1.77991626e+01, 1.78080130e+01,\n",
       "         1.78105980e+01, 1.78281692e+01, 1.78998361e+01, 1.79633794e+01,\n",
       "         1.80027863e+01, 1.81424864e+01, 1.81548901e+01, 1.82143692e+01,\n",
       "         1.83206057e+01, 1.83472977e+01, 1.83653364e+01, 1.84560004e+01,\n",
       "         1.85534328e+01, 1.86782191e+01, 1.86996754e+01, 1.88551617e+01,\n",
       "         1.90013823e+01, 1.91185261e+01, 1.92193878e+01, 1.92307660e+01,\n",
       "         1.92671698e+01, 1.92981421e+01, 1.93121669e+01, 1.93274579e+01,\n",
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       "         1.96311687e+01, 1.96539214e+01, 1.97000687e+01, 1.97280364e+01,\n",
       "         1.97468550e+01, 1.98297244e+01, 1.99744682e+01, 2.00253216e+01,\n",
       "         2.00878831e+01, 2.01414924e+01, 2.02208462e+01, 2.02385055e+01,\n",
       "         2.02554571e+01, 2.02572221e+01, 2.02849888e+01, 2.03567152e+01,\n",
       "         2.03626200e+01, 2.06540305e+01, 2.08537417e+01, 2.09066384e+01,\n",
       "         2.10776094e+01, 2.10902250e+01, 2.11179571e+01, 2.11826183e+01,\n",
       "         2.12560064e+01, 2.12902405e+01, 2.13192846e+01, 2.13355269e+01,\n",
       "         2.13507051e+01, 2.13606487e+01, 2.13671599e+01, 2.14389506e+01,\n",
       "         2.15957584e+01, 2.16534560e+01, 2.19061484e+01, 2.19099021e+01,\n",
       "         2.19669908e+01, 2.21183120e+01, 2.21318271e+01, 2.21671023e+01,\n",
       "         2.21897048e+01, 2.22076953e+01, 2.22288275e+01, 2.22497433e+01,\n",
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       "         2.29019443e+01, 2.29135037e+01, 2.29839123e+01, 2.30329931e+01,\n",
       "         2.30883014e+01, 2.31656021e+01, 2.31796661e+01, 2.32037084e+01,\n",
       "         2.32600290e+01, 2.33169826e+01, 2.36443784e+01, 2.36622050e+01,\n",
       "         2.36698503e+01, 2.37174940e+01, 2.37944519e+01, 2.38516246e+01,\n",
       "         2.38775063e+01, 2.39544104e+01, 2.39992869e+01, 2.40764030e+01,\n",
       "         2.40854337e+01, 2.41241048e+01, 2.42379907e+01, 2.42513600e+01,\n",
       "         2.42882898e+01, 2.44926427e+01, 2.45628127e+01, 2.46068820e+01,\n",
       "         2.46228018e+01, 2.46562132e+01, 2.47775500e+01, 2.48190737e+01,\n",
       "         2.49130402e+01, 2.49740187e+01, 2.50016110e+01, 2.50277897e+01,\n",
       "         2.50350084e+01, 2.54650463e+01, 2.55022739e+01, 2.56041855e+01,\n",
       "         2.56042235e+01, 2.56206444e+01, 2.56404722e+01, 2.58753846e+01,\n",
       "         2.59640713e+01, 2.60382271e+01, 2.60823796e+01, 2.61046307e+01,\n",
       "         2.62562322e+01, 2.63493237e+01, 2.63551769e+01, 2.65217953e+01,\n",
       "         2.65537524e+01, 2.66690048e+01, 2.66871913e+01, 2.68322699e+01,\n",
       "         2.68670540e+01, 2.70354903e+01, 2.70968535e+01, 2.71739583e+01,\n",
       "         2.72663855e+01, 2.73198090e+01, 2.74131851e+01, 2.74273348e+01,\n",
       "         2.75778068e+01, 2.76149395e+01, 2.78784468e+01, 2.80320598e+01,\n",
       "         2.80485477e+01, 2.80841638e+01, 2.81293887e+01, 2.84665918e+01,\n",
       "         2.84992798e+01, 2.85196056e+01, 2.85954088e+01, 2.86781476e+01,\n",
       "         2.87981903e+01, 2.88404024e+01, 2.89935714e+01, 2.90229733e+01,\n",
       "         2.91849071e+01, 2.92434742e+01, 2.92801685e+01, 2.94561537e+01,\n",
       "         2.95174596e+01, 2.95369620e+01, 2.95492573e+01, 2.96662926e+01,\n",
       "         2.98028959e+01, 2.98830315e+01, 2.99053727e+01, 2.99127631e+01,\n",
       "         2.99199583e+01, 3.00343238e+01, 3.03099753e+01, 3.06395433e+01,\n",
       "         3.06633039e+01, 3.08544945e+01, 3.08667828e+01, 3.09655394e+01,\n",
       "         3.10073308e+01, 3.10827433e+01, 3.11251283e+01, 3.11581754e+01,\n",
       "         3.12772913e+01, 3.13549588e+01, 3.13555470e+01, 3.13795169e+01,\n",
       "         3.13912217e+01, 3.13987952e+01, 3.15618409e+01, 3.16214716e+01,\n",
       "         3.17740860e+01, 3.18153004e+01, 3.18395298e+01, 3.18722848e+01,\n",
       "         3.20237147e+01, 3.21812300e+01, 3.22037855e+01, 3.23408348e+01,\n",
       "         3.24745738e+01, 3.25517317e+01, 3.26263109e+01, 3.27414663e+01,\n",
       "         3.28838279e+01, 3.29860301e+01, 3.30232427e+01, 3.30725264e+01,\n",
       "         3.31445669e+01, 3.32356176e+01, 3.33941912e+01, 3.37186966e+01,\n",
       "         3.37397450e+01, 3.39367477e+01, 3.39534739e+01, 3.39557636e+01,\n",
       "         3.41919988e+01, 3.42850826e+01, 3.44585045e+01, 3.45764691e+01,\n",
       "         3.45941423e+01, 3.46145054e+01, 3.46326117e+01, 3.46815263e+01,\n",
       "         3.47878002e+01, 3.49364397e+01, 3.49455674e+01, 3.51026108e+01,\n",
       "         3.53449875e+01, 3.55331638e+01, 3.56813932e+01, 3.57202037e+01,\n",
       "         3.57826445e+01, 3.58244778e+01, 3.58795575e+01, 3.59708797e+01,\n",
       "         3.60640197e+01, 3.65980366e+01, 3.66275105e+01, 3.66387364e+01,\n",
       "         3.67511884e+01, 3.68304443e+01, 3.68860927e+01, 3.69478319e+01,\n",
       "         3.71511551e+01, 3.73007334e+01, 3.73655620e+01, 3.76624187e+01,\n",
       "         3.77642752e+01, 3.78690467e+01, 3.80566050e+01, 3.81970837e+01,\n",
       "         3.82297518e+01, 3.82685976e+01, 3.82766379e+01, 3.84883836e+01,\n",
       "         3.85173033e+01, 3.85693524e+01, 3.85862784e+01, 3.86346738e+01,\n",
       "         3.86583098e+01, 3.88722239e+01, 3.89371789e+01, 3.89684818e+01,\n",
       "         3.89839413e+01, 3.93565582e+01, 3.93580306e+01, 3.93777314e+01,\n",
       "         3.94900859e+01, 3.96773354e+01, 3.97496871e+01, 3.99499316e+01,\n",
       "         4.00273995e+01, 4.00670982e+01, 4.01099022e+01, 4.01743090e+01,\n",
       "         4.04945992e+01, 4.05652259e+01, 4.07915374e+01, 4.07985556e+01,\n",
       "         4.08687669e+01, 4.10153440e+01, 4.10177001e+01, 4.10285256e+01,\n",
       "         4.10715058e+01, 4.11593554e+01, 4.12606281e+01, 4.12631530e+01,\n",
       "         4.13137669e+01, 4.13457607e+01, 4.13929028e+01, 4.16865797e+01,\n",
       "         4.18261805e+01, 4.18265254e+01, 4.18670411e+01, 4.19986586e+01,\n",
       "         4.23511732e+01, 4.25035471e+01, 4.25048646e+01, 4.25159177e+01,\n",
       "         4.25749514e+01, 4.25929491e+01, 4.27570470e+01, 4.30097115e+01,\n",
       "         4.30727572e+01, 4.33482777e+01, 4.34361776e+01, 4.34668420e+01,\n",
       "         4.35106200e+01, 4.35614037e+01, 4.38677590e+01, 4.39396503e+01,\n",
       "         4.39799979e+01, 4.39937066e+01, 4.40726033e+01, 4.42240626e+01,\n",
       "         4.43246619e+01, 4.46161067e+01, 4.46256106e+01, 4.51218308e+01,\n",
       "         4.53842936e+01, 4.54466239e+01, 4.56191000e+01, 4.56433798e+01,\n",
       "         4.58091596e+01, 4.59093368e+01, 4.59996921e+01, 4.60088508e+01,\n",
       "         4.60175197e+01, 4.61748072e+01, 4.64567696e+01, 4.64673732e+01,\n",
       "         4.65121818e+01, 4.65883297e+01, 4.66208534e+01, 4.69165258e+01,\n",
       "         4.71265716e+01, 4.71445695e+01, 4.72143217e+01, 4.73013740e+01,\n",
       "         4.73459578e+01, 4.74248313e+01, 4.77387840e+01, 4.78051918e+01,\n",
       "         4.78103479e+01, 4.81829931e+01, 4.82168345e+01, 4.84508821e+01,\n",
       "         4.84716147e+01, 4.84872044e+01, 4.86451714e+01, 4.90467837e+01,\n",
       "         4.91419796e+01, 4.92322667e+01, 4.93620553e+01, 4.93927678e+01,\n",
       "         4.99201294e+01, 5.03277248e+01, 5.03392348e+01, 5.05422318e+01,\n",
       "         5.07293863e+01, 5.10790153e+01, 5.10914817e+01, 5.11783410e+01,\n",
       "         5.13593427e+01, 5.13646115e+01, 5.14020900e+01, 5.14147010e+01,\n",
       "         5.14196136e+01, 5.17249712e+01, 5.17791856e+01, 5.18793753e+01,\n",
       "         5.20508995e+01, 5.21239108e+01, 5.21715973e+01, 5.23246691e+01,\n",
       "         5.23676850e+01, 5.25760809e+01, 5.26650892e+01, 5.31592310e+01,\n",
       "         5.39467009e+01, 5.41258734e+01, 5.42122554e+01, 5.44023361e+01,\n",
       "         5.45355182e+01, 5.47922302e+01, 5.48685055e+01, 5.49079371e+01,\n",
       "         5.49656460e+01, 5.51943592e+01, 5.54879801e+01, 5.56598625e+01,\n",
       "         5.56738207e+01, 5.57065285e+01, 5.58922059e+01, 5.62565791e+01,\n",
       "         5.62680774e+01, 5.62737747e+01, 5.64848586e+01, 5.68340140e+01,\n",
       "         5.68671335e+01, 5.71268083e+01, 5.72947632e+01, 5.72972280e+01,\n",
       "         5.81246658e+01, 5.84072671e+01, 5.84297336e+01, 5.84721458e+01,\n",
       "         5.85935016e+01, 5.89110819e+01, 5.89163851e+01, 5.90447152e+01,\n",
       "         5.92294960e+01, 5.98051708e+01, 6.01700174e+01, 6.02448733e+01,\n",
       "         6.08815905e+01, 6.09655932e+01, 6.12223718e+01, 6.12652011e+01,\n",
       "         6.17839537e+01, 6.21013722e+01, 6.23278481e+01, 6.24437161e+01,\n",
       "         6.27026773e+01, 6.31078118e+01, 6.32225381e+01, 6.34222779e+01,\n",
       "         6.34852404e+01, 6.37053335e+01, 6.37675839e+01, 6.39690217e+01,\n",
       "         6.46338030e+01, 6.53248905e+01, 6.57080656e+01, 6.57495681e+01,\n",
       "         6.59427290e+01, 6.60390993e+01, 6.63387969e+01, 6.63839746e+01,\n",
       "         6.64948206e+01, 6.66568752e+01, 6.66783402e+01, 6.67106663e+01,\n",
       "         6.74913842e+01, 6.74957930e+01, 6.77302790e+01, 6.80894629e+01,\n",
       "         6.86535171e+01, 6.90001383e+01, 6.93047541e+01, 6.95204720e+01,\n",
       "         6.97441329e+01, 7.01034757e+01, 7.08099614e+01, 7.15342768e+01,\n",
       "         7.15612646e+01, 7.20442340e+01, 7.20764168e+01, 7.23971509e+01,\n",
       "         7.24963364e+01, 7.27233838e+01, 7.29710941e+01, 7.33075633e+01,\n",
       "         7.36825971e+01, 7.37975773e+01, 7.41596642e+01, 7.52045103e+01,\n",
       "         7.54981718e+01, 7.57039089e+01, 7.58328359e+01, 7.59921950e+01,\n",
       "         7.68953237e+01, 7.69199079e+01, 7.72273240e+01, 7.74916702e+01,\n",
       "         7.76211458e+01, 7.84112135e+01, 7.87711475e+01, 7.90461218e+01,\n",
       "         7.93712055e+01, 7.94149020e+01, 8.04145995e+01, 8.06214646e+01,\n",
       "         8.06279021e+01, 8.08397928e+01, 8.13041994e+01, 8.14110506e+01,\n",
       "         8.19895709e+01, 8.28561492e+01, 8.50755114e+01, 8.50864117e+01,\n",
       "         8.51559975e+01, 8.53100546e+01, 8.55064524e+01, 8.57597547e+01,\n",
       "         8.74709713e+01, 8.79597793e+01, 8.82782787e+01, 8.83957157e+01,\n",
       "         8.89032981e+01, 8.90057368e+01, 8.94775923e+01, 9.04686614e+01,\n",
       "         9.18210153e+01, 9.22430611e+01, 9.43022946e+01, 9.43645424e+01,\n",
       "         9.44507476e+01, 9.57747725e+01, 9.60668981e+01, 9.64466681e+01,\n",
       "         9.67402687e+01, 9.76675217e+01, 9.95033834e+01, 1.00434132e+02,\n",
       "         1.01227456e+02, 1.01896860e+02, 1.02011650e+02, 1.02506097e+02,\n",
       "         1.02535226e+02, 1.04918870e+02, 1.06258028e+02, 1.10031282e+02,\n",
       "         1.11817794e+02, 1.13239088e+02, 1.13927365e+02, 1.13976978e+02,\n",
       "         1.15007274e+02, 1.15530744e+02, 1.16034837e+02, 1.16076270e+02,\n",
       "         1.16365179e+02, 1.18262605e+02, 1.21499598e+02, 1.24802465e+02,\n",
       "         1.25018989e+02, 1.26294255e+02, 1.27004668e+02, 1.28763371e+02,\n",
       "         1.29651866e+02, 1.30127611e+02, 1.30614195e+02, 1.32854295e+02,\n",
       "         1.39418772e+02, 1.44064976e+02, 1.47077310e+02, 1.56665279e+02,\n",
       "         1.58854159e+02, 1.84543974e+02, 1.93141579e+02, 1.96751229e+02])),\n",
       " (30.054434806886086, 0.08782922711992569, 0.9990430729895915))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(data, dist='expon', plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# beta distribution - proportions, naturally bounded distribution 0-1\n",
    "\n",
    "from scipy.stats import beta\n",
    "\n",
    "data = beta.rvs(a=2, b=5, size=1000)\n",
    "\n",
    "plt.hist(data, bins=30);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((array([0.00685914, 0.01074204, 0.01361607, 0.0160046 , 0.01809811,\n",
       "         0.0199879 , 0.02172612, 0.0233459 , 0.02486984, 0.02631416,\n",
       "         0.02769099, 0.02900964, 0.03027751, 0.03150051, 0.03268354,\n",
       "         0.03383063, 0.0349452 , 0.03603017, 0.03708803, 0.03812096,\n",
       "         0.03913085, 0.04011938, 0.04108803, 0.04203811, 0.04297081,\n",
       "         0.04388719, 0.0447882 , 0.04567472, 0.04654755, 0.04740739,\n",
       "         0.04825492, 0.04909075, 0.04991543, 0.05072949, 0.0515334 ,\n",
       "         0.05232762, 0.05311255, 0.05388859, 0.05465609, 0.05541539,\n",
       "         0.05616682, 0.05691066, 0.05764719, 0.05837669, 0.05909939,\n",
       "         0.05981554, 0.06052535, 0.06122903, 0.06192678, 0.0626188 ,\n",
       "         0.06330526, 0.06398633, 0.06466217, 0.06533294, 0.06599878,\n",
       "         0.06665984, 0.06731625, 0.06796814, 0.06861563, 0.06925884,\n",
       "         0.06989788, 0.07053286, 0.07116388, 0.07179104, 0.07241445,\n",
       "         0.07303418, 0.07365034, 0.074263  , 0.07487224, 0.07547815,\n",
       "         0.0760808 , 0.07668027, 0.07727663, 0.07786994, 0.07846027,\n",
       "         0.07904768, 0.07963225, 0.08021402, 0.08079305, 0.08136941,\n",
       "         0.08194314, 0.08251431, 0.08308295, 0.08364912, 0.08421287,\n",
       "         0.08477424, 0.08533328, 0.08589004, 0.08644455, 0.08699686,\n",
       "         0.08754701, 0.08809504, 0.08864098, 0.08918488, 0.08972677,\n",
       "         0.09026668, 0.09080465, 0.09134071, 0.0918749 , 0.09240724,\n",
       "         0.09293778, 0.09346653, 0.09399353, 0.09451881, 0.09504239,\n",
       "         0.09556431, 0.09608459, 0.09660325, 0.09712032, 0.09763583,\n",
       "         0.0981498 , 0.09866225, 0.09917321, 0.09968271, 0.10019075,\n",
       "         0.10069737, 0.10120259, 0.10170643, 0.1022089 , 0.10271003,\n",
       "         0.10320984, 0.10370835, 0.10420557, 0.10470153, 0.10519624,\n",
       "         0.10568972, 0.10618199, 0.10667307, 0.10716296, 0.1076517 ,\n",
       "         0.10813929, 0.10862575, 0.10911109, 0.10959534, 0.1100785 ,\n",
       "         0.1105606 , 0.11104164, 0.11152164, 0.11200061, 0.11247857,\n",
       "         0.11295553, 0.1134315 , 0.11390651, 0.11438055, 0.11485364,\n",
       "         0.1153258 , 0.11579703, 0.11626735, 0.11673678, 0.11720531,\n",
       "         0.11767297, 0.11813977, 0.1186057 , 0.1190708 , 0.11953506,\n",
       "         0.1199985 , 0.12046113, 0.12092295, 0.12138399, 0.12184424,\n",
       "         0.12230372, 0.12276243, 0.1232204 , 0.12367762, 0.1241341 ,\n",
       "         0.12458986, 0.1250449 , 0.12549923, 0.12595287, 0.12640581,\n",
       "         0.12685807, 0.12730965, 0.12776057, 0.12821083, 0.12866044,\n",
       "         0.12910941, 0.12955775, 0.13000546, 0.13045254, 0.13089902,\n",
       "         0.13134489, 0.13179017, 0.13223485, 0.13267895, 0.13312247,\n",
       "         0.13356543, 0.13400782, 0.13444966, 0.13489095, 0.13533169,\n",
       "         0.1357719 , 0.13621158, 0.13665074, 0.13708938, 0.13752751,\n",
       "         0.13796513, 0.13840225, 0.13883888, 0.13927503, 0.13971069,\n",
       "         0.14014588, 0.1405806 , 0.14101485, 0.14144864, 0.14188199,\n",
       "         0.14231488, 0.14274733, 0.14317934, 0.14361093, 0.14404208,\n",
       "         0.14447282, 0.14490314, 0.14533304, 0.14576254, 0.14619164,\n",
       "         0.14662035, 0.14704866, 0.14747658, 0.14790412, 0.14833129,\n",
       "         0.14875808, 0.1491845 , 0.14961056, 0.15003626, 0.15046161,\n",
       "         0.1508866 , 0.15131125, 0.15173556, 0.15215953, 0.15258317,\n",
       "         0.15300648, 0.15342946, 0.15385213, 0.15427447, 0.15469651,\n",
       "         0.15511823, 0.15553966, 0.15596078, 0.1563816 , 0.15680214,\n",
       "         0.15722238, 0.15764234, 0.15806202, 0.15848142, 0.15890055,\n",
       "         0.1593194 , 0.159738  , 0.16015632, 0.16057439, 0.16099221,\n",
       "         0.16140977, 0.16182708, 0.16224415, 0.16266098, 0.16307757,\n",
       "         0.16349392, 0.16391005, 0.16432594, 0.16474161, 0.16515706,\n",
       "         0.1655723 , 0.16598731, 0.16640212, 0.16681672, 0.16723111,\n",
       "         0.1676453 , 0.16805929, 0.16847309, 0.16888669, 0.1693001 ,\n",
       "         0.16971333, 0.17012637, 0.17053924, 0.17095192, 0.17136443,\n",
       "         0.17177677, 0.17218895, 0.17260095, 0.17301279, 0.17342448,\n",
       "         0.173836  , 0.17424738, 0.1746586 , 0.17506967, 0.17548059,\n",
       "         0.17589138, 0.17630202, 0.17671252, 0.1771229 , 0.17753313,\n",
       "         0.17794324, 0.17835322, 0.17876308, 0.17917282, 0.17958244,\n",
       "         0.17999194, 0.18040133, 0.1808106 , 0.18121977, 0.18162883,\n",
       "         0.18203779, 0.18244665, 0.18285541, 0.18326407, 0.18367264,\n",
       "         0.18408112, 0.18448952, 0.18489782, 0.18530604, 0.18571418,\n",
       "         0.18612225, 0.18653023, 0.18693814, 0.18734598, 0.18775376,\n",
       "         0.18816146, 0.1885691 , 0.18897668, 0.1893842 , 0.18979166,\n",
       "         0.19019906, 0.19060642, 0.19101372, 0.19142097, 0.19182818,\n",
       "         0.19223535, 0.19264247, 0.19304955, 0.1934566 , 0.19386361,\n",
       "         0.19427059, 0.19467754, 0.19508446, 0.19549136, 0.19589823,\n",
       "         0.19630508, 0.19671191, 0.19711873, 0.19752553, 0.19793231,\n",
       "         0.19833909, 0.19874585, 0.19915261, 0.19955937, 0.19996612,\n",
       "         0.20037287, 0.20077963, 0.20118639, 0.20159315, 0.20199992,\n",
       "         0.20240671, 0.2028135 , 0.20322031, 0.20362714, 0.20403399,\n",
       "         0.20444085, 0.20484774, 0.20525465, 0.20566159, 0.20606856,\n",
       "         0.20647556, 0.20688259, 0.20728966, 0.20769676, 0.2081039 ,\n",
       "         0.20851108, 0.20891831, 0.20932558, 0.2097329 , 0.21014026,\n",
       "         0.21054768, 0.21095515, 0.21136267, 0.21177025, 0.21217789,\n",
       "         0.21258559, 0.21299335, 0.21340118, 0.21380907, 0.21421703,\n",
       "         0.21462506, 0.21503317, 0.21544135, 0.2158496 , 0.21625793,\n",
       "         0.21666634, 0.21707484, 0.21748341, 0.21789208, 0.21830083,\n",
       "         0.21870967, 0.2191186 , 0.21952763, 0.21993675, 0.22034597,\n",
       "         0.22075529, 0.2211647 , 0.22157423, 0.22198385, 0.22239359,\n",
       "         0.22280343, 0.22321338, 0.22362345, 0.22403363, 0.22444392,\n",
       "         0.22485434, 0.22526487, 0.22567553, 0.22608631, 0.22649721,\n",
       "         0.22690825, 0.22731941, 0.22773071, 0.22814213, 0.2285537 ,\n",
       "         0.2289654 , 0.22937724, 0.22978922, 0.23020134, 0.23061361,\n",
       "         0.23102603, 0.23143859, 0.23185131, 0.23226417, 0.23267719,\n",
       "         0.23309037, 0.23350371, 0.2339172 , 0.23433086, 0.23474468,\n",
       "         0.23515867, 0.23557282, 0.23598715, 0.23640164, 0.23681631,\n",
       "         0.23723115, 0.23764617, 0.23806137, 0.23847675, 0.23889232,\n",
       "         0.23930807, 0.239724  , 0.24014012, 0.24055644, 0.24097294,\n",
       "         0.24138965, 0.24180654, 0.24222364, 0.24264093, 0.24305843,\n",
       "         0.24347613, 0.24389404, 0.24431216, 0.24473048, 0.24514902,\n",
       "         0.24556777, 0.24598674, 0.24640593, 0.24682533, 0.24724496,\n",
       "         0.24766481, 0.24808488, 0.24850519, 0.24892572, 0.24934648,\n",
       "         0.24976748, 0.25018871, 0.25061018, 0.25103189, 0.25145385,\n",
       "         0.25187604, 0.25229848, 0.25272117, 0.25314411, 0.2535673 ,\n",
       "         0.25399074, 0.25441444, 0.25483839, 0.25526261, 0.25568709,\n",
       "         0.25611183, 0.25653684, 0.25696211, 0.25738766, 0.25781347,\n",
       "         0.25823956, 0.25866593, 0.25909258, 0.2595195 , 0.25994671,\n",
       "         0.2603742 , 0.26080198, 0.26123005, 0.26165841, 0.26208706,\n",
       "         0.26251601, 0.26294526, 0.2633748 , 0.26380464, 0.26423479,\n",
       "         0.26466525, 0.26509601, 0.26552709, 0.26595847, 0.26639017,\n",
       "         0.26682219, 0.26725453, 0.26768718, 0.26812016, 0.26855347,\n",
       "         0.26898711, 0.26942107, 0.26985537, 0.27029   , 0.27072497,\n",
       "         0.27116027, 0.27159592, 0.27203192, 0.27246825, 0.27290494,\n",
       "         0.27334198, 0.27377937, 0.27421711, 0.27465522, 0.27509368,\n",
       "         0.27553251, 0.2759717 , 0.27641125, 0.27685118, 0.27729148,\n",
       "         0.27773215, 0.2781732 , 0.27861463, 0.27905644, 0.27949863,\n",
       "         0.27994121, 0.28038418, 0.28082754, 0.28127129, 0.28171544,\n",
       "         0.28215999, 0.28260494, 0.28305029, 0.28349605, 0.28394222,\n",
       "         0.2843888 , 0.28483579, 0.2852832 , 0.28573103, 0.28617928,\n",
       "         0.28662795, 0.28707705, 0.28752658, 0.28797655, 0.28842694,\n",
       "         0.28887778, 0.28932905, 0.28978077, 0.29023294, 0.29068555,\n",
       "         0.29113861, 0.29159213, 0.2920461 , 0.29250053, 0.29295542,\n",
       "         0.29341078, 0.29386661, 0.29432291, 0.29477968, 0.29523692,\n",
       "         0.29569465, 0.29615285, 0.29661155, 0.29707073, 0.2975304 ,\n",
       "         0.29799056, 0.29845122, 0.29891238, 0.29937404, 0.29983621,\n",
       "         0.30029888, 0.30076207, 0.30122577, 0.30168999, 0.30215473,\n",
       "         0.30262   , 0.30308579, 0.30355211, 0.30401896, 0.30448635,\n",
       "         0.30495428, 0.30542275, 0.30589177, 0.30636134, 0.30683146,\n",
       "         0.30730214, 0.30777337, 0.30824517, 0.30871753, 0.30919046,\n",
       "         0.30966397, 0.31013805, 0.31061271, 0.31108795, 0.31156378,\n",
       "         0.3120402 , 0.31251721, 0.31299481, 0.31347302, 0.31395183,\n",
       "         0.31443125, 0.31491128, 0.31539192, 0.31587318, 0.31635507,\n",
       "         0.31683758, 0.31732071, 0.31780448, 0.31828889, 0.31877394,\n",
       "         0.31925963, 0.31974597, 0.32023296, 0.32072061, 0.32120892,\n",
       "         0.32169789, 0.32218753, 0.32267784, 0.32316883, 0.32366049,\n",
       "         0.32415284, 0.32464588, 0.32513961, 0.32563404, 0.32612916,\n",
       "         0.32662499, 0.32712153, 0.32761878, 0.32811675, 0.32861545,\n",
       "         0.32911486, 0.32961501, 0.33011589, 0.33061751, 0.33111988,\n",
       "         0.33162299, 0.33212686, 0.33263148, 0.33313686, 0.33364302,\n",
       "         0.33414994, 0.33465764, 0.33516612, 0.33567538, 0.33618543,\n",
       "         0.33669628, 0.33720793, 0.33772039, 0.33823365, 0.33874773,\n",
       "         0.33926263, 0.33977835, 0.34029491, 0.34081229, 0.34133052,\n",
       "         0.3418496 , 0.34236952, 0.3428903 , 0.34341195, 0.34393446,\n",
       "         0.34445784, 0.3449821 , 0.34550724, 0.34603327, 0.3465602 ,\n",
       "         0.34708802, 0.34761675, 0.3481464 , 0.34867696, 0.34920844,\n",
       "         0.34974085, 0.3502742 , 0.35080848, 0.35134372, 0.35187991,\n",
       "         0.35241705, 0.35295516, 0.35349425, 0.35403431, 0.35457535,\n",
       "         0.35511739, 0.35566042, 0.35620445, 0.3567495 , 0.35729556,\n",
       "         0.35784264, 0.35839076, 0.35893991, 0.35949011, 0.36004135,\n",
       "         0.36059365, 0.36114702, 0.36170146, 0.36225698, 0.36281358,\n",
       "         0.36337127, 0.36393007, 0.36448997, 0.36505099, 0.36561314,\n",
       "         0.36617641, 0.36674082, 0.36730638, 0.36787309, 0.36844096,\n",
       "         0.36901   , 0.36958022, 0.37015163, 0.37072422, 0.37129803,\n",
       "         0.37187304, 0.37244927, 0.37302673, 0.37360542, 0.37418536,\n",
       "         0.37476655, 0.37534901, 0.37593274, 0.37651774, 0.37710404,\n",
       "         0.37769164, 0.37828054, 0.37887076, 0.37946231, 0.38005519,\n",
       "         0.38064942, 0.38124501, 0.38184196, 0.38244029, 0.38304   ,\n",
       "         0.38364111, 0.38424363, 0.38484756, 0.38545292, 0.38605972,\n",
       "         0.38666797, 0.38727767, 0.38788885, 0.38850151, 0.38911566,\n",
       "         0.38973132, 0.39034849, 0.39096719, 0.39158742, 0.39220921,\n",
       "         0.39283256, 0.39345749, 0.394084  , 0.39471211, 0.39534183,\n",
       "         0.39597318, 0.39660616, 0.3972408 , 0.3978771 , 0.39851507,\n",
       "         0.39915473, 0.3997961 , 0.40043919, 0.401084  , 0.40173056,\n",
       "         0.40237888, 0.40302898, 0.40368086, 0.40433454, 0.40499004,\n",
       "         0.40564738, 0.40630656, 0.40696761, 0.40763053, 0.40829535,\n",
       "         0.40896208, 0.40963074, 0.41030134, 0.4109739 , 0.41164844,\n",
       "         0.41232497, 0.41300352, 0.41368409, 0.41436671, 0.41505139,\n",
       "         0.41573816, 0.41642702, 0.41711801, 0.41781113, 0.41850641,\n",
       "         0.41920387, 0.41990353, 0.4206054 , 0.42130951, 0.42201588,\n",
       "         0.42272452, 0.42343547, 0.42414873, 0.42486434, 0.42558231,\n",
       "         0.42630267, 0.42702543, 0.42775063, 0.42847828, 0.42920841,\n",
       "         0.42994104, 0.4306762 , 0.43141391, 0.4321542 , 0.43289709,\n",
       "         0.4336426 , 0.43439077, 0.43514162, 0.43589517, 0.43665146,\n",
       "         0.43741051, 0.43817235, 0.43893701, 0.43970451, 0.44047489,\n",
       "         0.44124818, 0.4420244 , 0.44280359, 0.44358578, 0.444371  ,\n",
       "         0.44515929, 0.44595067, 0.44674518, 0.44754285, 0.44834372,\n",
       "         0.44914782, 0.44995519, 0.45076587, 0.45157989, 0.45239729,\n",
       "         0.45321811, 0.45404238, 0.45487015, 0.45570146, 0.45653634,\n",
       "         0.45737485, 0.45821701, 0.45906288, 0.4599125 , 0.46076591,\n",
       "         0.46162316, 0.4624843 , 0.46334937, 0.46421842, 0.4650915 ,\n",
       "         0.46596866, 0.46684995, 0.46773543, 0.46862514, 0.46951914,\n",
       "         0.47041749, 0.47132024, 0.47222745, 0.47313917, 0.47405547,\n",
       "         0.47497641, 0.47590205, 0.47683245, 0.47776768, 0.47870781,\n",
       "         0.4796529 , 0.48060301, 0.48155823, 0.48251862, 0.48348426,\n",
       "         0.48445522, 0.48543158, 0.48641341, 0.48740081, 0.48839384,\n",
       "         0.48939259, 0.49039716, 0.49140762, 0.49242408, 0.49344661,\n",
       "         0.49447531, 0.49551029, 0.49655164, 0.49759946, 0.49865385,\n",
       "         0.49971493, 0.5007828 , 0.50185758, 0.50293937, 0.5040283 ,\n",
       "         0.50512449, 0.50622807, 0.50733915, 0.50845788, 0.50958439,\n",
       "         0.51071881, 0.51186128, 0.51301196, 0.514171  , 0.51533855,\n",
       "         0.51651476, 0.51769981, 0.51889387, 0.52009709, 0.52130968,\n",
       "         0.5225318 , 0.52376366, 0.52500544, 0.52625736, 0.52751961,\n",
       "         0.52879242, 0.53007601, 0.53137061, 0.53267646, 0.5339938 ,\n",
       "         0.5353229 , 0.536664  , 0.5380174 , 0.53938336, 0.54076219,\n",
       "         0.54215419, 0.54355967, 0.54497897, 0.54641241, 0.54786037,\n",
       "         0.54932319, 0.55080127, 0.552295  , 0.5538048 , 0.55533109,\n",
       "         0.55687433, 0.55843499, 0.56001356, 0.56161054, 0.56322647,\n",
       "         0.56486192, 0.56651746, 0.56819371, 0.56989131, 0.57161094,\n",
       "         0.57335331, 0.57511915, 0.57690926, 0.57872446, 0.58056562,\n",
       "         0.58243366, 0.58432954, 0.58625429, 0.58820901, 0.59019483,\n",
       "         0.59221297, 0.59426475, 0.59635153, 0.5984748 , 0.60063611,\n",
       "         0.60283715, 0.60507973, 0.60736575, 0.60969731, 0.61207662,\n",
       "         0.6145061 , 0.61698834, 0.61952617, 0.62212264, 0.6247811 ,\n",
       "         0.62750517, 0.63029884, 0.63316649, 0.63611294, 0.63914352,\n",
       "         0.64226415, 0.64548142, 0.64880273, 0.65223637, 0.65579174,\n",
       "         0.65947951, 0.66331191, 0.66730302, 0.67146918, 0.67582954,\n",
       "         0.68040672, 0.68522779, 0.69032545, 0.69573985, 0.70152105,\n",
       "         0.70773272, 0.71445764, 0.72180658, 0.72993284, 0.73905818,\n",
       "         0.74952245, 0.76188992, 0.77721593, 0.79790892, 0.83188169]),\n",
       "  array([0.01505691, 0.01641901, 0.01782046, 0.02030331, 0.02131245,\n",
       "         0.02201103, 0.02292662, 0.02476642, 0.02667719, 0.02916633,\n",
       "         0.03144981, 0.03286038, 0.03446143, 0.03492871, 0.03715594,\n",
       "         0.03727285, 0.0392056 , 0.04102205, 0.04123788, 0.04441652,\n",
       "         0.04445603, 0.04584373, 0.0462082 , 0.04634946, 0.04899183,\n",
       "         0.04921573, 0.05132297, 0.05140619, 0.05168106, 0.05211099,\n",
       "         0.05229726, 0.05236456, 0.05243074, 0.05263015, 0.05296962,\n",
       "         0.05396043, 0.05456071, 0.05492454, 0.05671847, 0.05701133,\n",
       "         0.05728856, 0.05756571, 0.05781065, 0.057963  , 0.05925718,\n",
       "         0.05961168, 0.05988857, 0.06004662, 0.0600524 , 0.06272892,\n",
       "         0.06323454, 0.06332828, 0.06373337, 0.06386303, 0.06393234,\n",
       "         0.06455359, 0.06501863, 0.06685095, 0.06710708, 0.06762612,\n",
       "         0.06810702, 0.06856864, 0.06882145, 0.06934071, 0.07005233,\n",
       "         0.07058389, 0.07067293, 0.07071644, 0.07194524, 0.07269866,\n",
       "         0.07282377, 0.07327117, 0.07346637, 0.07355095, 0.07387992,\n",
       "         0.0754666 , 0.07680663, 0.0776591 , 0.07789551, 0.08053306,\n",
       "         0.08112599, 0.08175527, 0.08189314, 0.08294604, 0.08335932,\n",
       "         0.0835549 , 0.08371321, 0.08392699, 0.08609954, 0.08716708,\n",
       "         0.08725225, 0.08924496, 0.08934764, 0.09051039, 0.09101332,\n",
       "         0.09115245, 0.09179397, 0.09252084, 0.09415567, 0.09679793,\n",
       "         0.09704771, 0.09786996, 0.09810948, 0.09885196, 0.09925503,\n",
       "         0.0995024 , 0.10037541, 0.1005473 , 0.10115428, 0.10123019,\n",
       "         0.10128156, 0.10129365, 0.10145494, 0.10175645, 0.10177313,\n",
       "         0.1024374 , 0.10253074, 0.10309194, 0.10327568, 0.10422422,\n",
       "         0.10499398, 0.10534292, 0.10580941, 0.10604627, 0.10606784,\n",
       "         0.10655106, 0.10821297, 0.10868162, 0.11037603, 0.11080935,\n",
       "         0.11088972, 0.11110313, 0.11131633, 0.11164289, 0.11166193,\n",
       "         0.11298962, 0.11335279, 0.11371962, 0.11395554, 0.11404296,\n",
       "         0.11442265, 0.11535075, 0.11552275, 0.11557828, 0.11557985,\n",
       "         0.11664116, 0.11668748, 0.11781596, 0.11972863, 0.1203648 ,\n",
       "         0.12076985, 0.12097408, 0.12113915, 0.12152284, 0.12178142,\n",
       "         0.12295906, 0.12316852, 0.1236541 , 0.12416318, 0.12463711,\n",
       "         0.12502749, 0.12557761, 0.12585526, 0.12669233, 0.12719443,\n",
       "         0.12729897, 0.12796229, 0.12854236, 0.12917073, 0.12963974,\n",
       "         0.12978993, 0.13016988, 0.1303596 , 0.13049734, 0.13088887,\n",
       "         0.13186993, 0.13264496, 0.13339452, 0.13372377, 0.13379361,\n",
       "         0.13422659, 0.13457945, 0.13562262, 0.13598095, 0.13643888,\n",
       "         0.13649014, 0.13682966, 0.13782121, 0.1380421 , 0.13830997,\n",
       "         0.13891796, 0.13922269, 0.13936665, 0.13959769, 0.13972391,\n",
       "         0.14096005, 0.14114809, 0.14131728, 0.14160786, 0.14168872,\n",
       "         0.14176471, 0.14178137, 0.14317545, 0.14329656, 0.14393015,\n",
       "         0.14403569, 0.14420955, 0.14469654, 0.14530342, 0.14574727,\n",
       "         0.14668221, 0.14761238, 0.14782348, 0.14790397, 0.14855828,\n",
       "         0.14924107, 0.1493427 , 0.15136872, 0.15179928, 0.15182611,\n",
       "         0.15226287, 0.15254109, 0.15362227, 0.15375102, 0.15384576,\n",
       "         0.15404623, 0.15475539, 0.15504035, 0.15555017, 0.15567571,\n",
       "         0.15614902, 0.15645675, 0.15706688, 0.157128  , 0.15741419,\n",
       "         0.15787787, 0.15809389, 0.15836092, 0.15849444, 0.15893512,\n",
       "         0.15948276, 0.15974632, 0.16110463, 0.16124914, 0.16144954,\n",
       "         0.16189051, 0.16204868, 0.16219546, 0.16268235, 0.16296166,\n",
       "         0.16302246, 0.16397607, 0.16423878, 0.16425407, 0.16439406,\n",
       "         0.16455576, 0.16469772, 0.16517059, 0.1652813 , 0.16542073,\n",
       "         0.16555601, 0.16634599, 0.16772569, 0.1680979 , 0.16851789,\n",
       "         0.16864942, 0.16889775, 0.16904192, 0.1693585 , 0.16946906,\n",
       "         0.17021979, 0.17029901, 0.17032272, 0.17086141, 0.17100815,\n",
       "         0.17104179, 0.17109772, 0.17199095, 0.1720256 , 0.17213876,\n",
       "         0.17217266, 0.17256683, 0.17330081, 0.1738126 , 0.17552809,\n",
       "         0.17623217, 0.17671093, 0.17689071, 0.17690823, 0.17715414,\n",
       "         0.17720912, 0.17739558, 0.17748602, 0.17755208, 0.17767134,\n",
       "         0.17952151, 0.17962286, 0.18001015, 0.18030252, 0.18057896,\n",
       "         0.18065722, 0.18135447, 0.18138478, 0.18144471, 0.18220128,\n",
       "         0.18240047, 0.18302192, 0.18339598, 0.18511005, 0.18537253,\n",
       "         0.18620852, 0.18707154, 0.18760273, 0.18800182, 0.18805205,\n",
       "         0.18865879, 0.18873715, 0.18934054, 0.18964633, 0.19105238,\n",
       "         0.19127272, 0.19204597, 0.19341191, 0.19354568, 0.19409092,\n",
       "         0.19436518, 0.19459966, 0.19526203, 0.19545968, 0.19554301,\n",
       "         0.19559427, 0.19567719, 0.19585307, 0.19595372, 0.19615511,\n",
       "         0.19616775, 0.19630809, 0.19676715, 0.19736005, 0.19749035,\n",
       "         0.19765868, 0.19781365, 0.19809822, 0.19901222, 0.19906223,\n",
       "         0.19967471, 0.20049153, 0.20062038, 0.2018108 , 0.20241748,\n",
       "         0.20245495, 0.20259775, 0.20401637, 0.20475639, 0.20497718,\n",
       "         0.20551263, 0.20574423, 0.20586064, 0.20652641, 0.20699487,\n",
       "         0.2077022 , 0.20772244, 0.20817511, 0.20840699, 0.20900891,\n",
       "         0.20953902, 0.21065532, 0.21102989, 0.21144613, 0.21161954,\n",
       "         0.21203298, 0.21215056, 0.21250339, 0.21337675, 0.21349729,\n",
       "         0.21364707, 0.21527311, 0.21527729, 0.21568779, 0.21568966,\n",
       "         0.21593926, 0.21619561, 0.2175284 , 0.21771457, 0.21774097,\n",
       "         0.21818523, 0.21833691, 0.21981714, 0.21988092, 0.22033938,\n",
       "         0.22059337, 0.2206401 , 0.22067582, 0.22149951, 0.22152311,\n",
       "         0.22212749, 0.22232726, 0.2224796 , 0.22292116, 0.22441149,\n",
       "         0.22500454, 0.22510002, 0.22549047, 0.22569079, 0.22634554,\n",
       "         0.22660527, 0.22779318, 0.22816462, 0.22819182, 0.22907858,\n",
       "         0.22960441, 0.22967218, 0.2297183 , 0.23067534, 0.23069909,\n",
       "         0.23113511, 0.23116491, 0.2319816 , 0.23257057, 0.23400238,\n",
       "         0.23461525, 0.23481799, 0.23525035, 0.23533085, 0.23597218,\n",
       "         0.23633649, 0.23691144, 0.23703757, 0.23706405, 0.2376349 ,\n",
       "         0.23866607, 0.2387585 , 0.23967614, 0.23982741, 0.24175832,\n",
       "         0.2419782 , 0.24235519, 0.24308096, 0.24338173, 0.24391908,\n",
       "         0.24393919, 0.24404118, 0.24405576, 0.24516966, 0.24571515,\n",
       "         0.24575575, 0.24584907, 0.24588633, 0.24639943, 0.24906182,\n",
       "         0.2495652 , 0.24961501, 0.24990504, 0.2500678 , 0.25041974,\n",
       "         0.25090729, 0.25223552, 0.25232542, 0.25263618, 0.25292976,\n",
       "         0.25296226, 0.25319355, 0.25342322, 0.25414379, 0.25434603,\n",
       "         0.25451557, 0.25458097, 0.25476856, 0.25559932, 0.25579677,\n",
       "         0.25599731, 0.25634148, 0.25728988, 0.25783852, 0.25817159,\n",
       "         0.25827734, 0.25854664, 0.25907714, 0.25961465, 0.26139015,\n",
       "         0.26207506, 0.26225555, 0.26279244, 0.26417414, 0.26428878,\n",
       "         0.26429811, 0.26465946, 0.26543086, 0.26566109, 0.26568441,\n",
       "         0.26574411, 0.26583922, 0.26591618, 0.26626982, 0.26627857,\n",
       "         0.2672957 , 0.26755536, 0.26836205, 0.26883759, 0.26949146,\n",
       "         0.26955609, 0.26965123, 0.2699362 , 0.27059472, 0.27072112,\n",
       "         0.27101787, 0.27194681, 0.27227138, 0.2732511 , 0.27369085,\n",
       "         0.27396489, 0.27404599, 0.27407077, 0.27460256, 0.27491964,\n",
       "         0.27503679, 0.27520364, 0.27549122, 0.27576315, 0.27595709,\n",
       "         0.27740905, 0.27741136, 0.27757258, 0.27786306, 0.27824512,\n",
       "         0.2784643 , 0.27862651, 0.27876741, 0.27879545, 0.27919104,\n",
       "         0.2802787 , 0.28040688, 0.28175191, 0.28194362, 0.28232041,\n",
       "         0.28235124, 0.28242716, 0.28273771, 0.28326197, 0.28334211,\n",
       "         0.28415897, 0.2843041 , 0.28437466, 0.28504625, 0.2851112 ,\n",
       "         0.28554726, 0.28560181, 0.28564047, 0.28572553, 0.28572871,\n",
       "         0.28713482, 0.28725219, 0.2877922 , 0.28788879, 0.28789968,\n",
       "         0.28838199, 0.28847495, 0.28943846, 0.290293  , 0.29048645,\n",
       "         0.29076547, 0.29087406, 0.2911791 , 0.29133447, 0.29202479,\n",
       "         0.29314318, 0.29344741, 0.29368503, 0.2937271 , 0.29415457,\n",
       "         0.29453341, 0.29706618, 0.29763871, 0.29789804, 0.29890351,\n",
       "         0.2990962 , 0.29975228, 0.30021782, 0.30226766, 0.30239878,\n",
       "         0.30271282, 0.30326121, 0.30333252, 0.30336307, 0.30453805,\n",
       "         0.30489309, 0.3050552 , 0.30563795, 0.30601888, 0.30642249,\n",
       "         0.30685376, 0.30731443, 0.30763582, 0.30841706, 0.31015427,\n",
       "         0.31133888, 0.31135878, 0.3117137 , 0.31234817, 0.3123799 ,\n",
       "         0.31263919, 0.31348898, 0.31523734, 0.31543762, 0.31577659,\n",
       "         0.3158121 , 0.31631926, 0.31647299, 0.31722889, 0.31766128,\n",
       "         0.31854225, 0.31886829, 0.31912705, 0.31928012, 0.320318  ,\n",
       "         0.32085024, 0.32118136, 0.32121053, 0.32141982, 0.32269963,\n",
       "         0.32295998, 0.32327752, 0.32367753, 0.32384961, 0.32395454,\n",
       "         0.32602201, 0.32747154, 0.32797554, 0.32798788, 0.32809995,\n",
       "         0.32830601, 0.3285634 , 0.32881985, 0.32922425, 0.32953216,\n",
       "         0.33006046, 0.33076164, 0.33098967, 0.33130649, 0.33150526,\n",
       "         0.33163046, 0.33169887, 0.33185128, 0.33236159, 0.33247173,\n",
       "         0.33303657, 0.33321001, 0.33454775, 0.33462441, 0.334667  ,\n",
       "         0.33494186, 0.33509593, 0.33515175, 0.33527676, 0.33554628,\n",
       "         0.3360862 , 0.33682693, 0.3369829 , 0.33820948, 0.33838854,\n",
       "         0.33861262, 0.33983094, 0.34049625, 0.34127412, 0.34154388,\n",
       "         0.34264582, 0.34270951, 0.34282986, 0.34346872, 0.34372273,\n",
       "         0.34383153, 0.34431975, 0.34461508, 0.34490717, 0.34494266,\n",
       "         0.34504151, 0.34533071, 0.34533281, 0.34566794, 0.34584144,\n",
       "         0.34604084, 0.34625685, 0.34729009, 0.34790515, 0.3490216 ,\n",
       "         0.34939555, 0.34994991, 0.34995316, 0.34998787, 0.3501823 ,\n",
       "         0.35027841, 0.35122234, 0.35153324, 0.35333834, 0.3534758 ,\n",
       "         0.35408925, 0.35452887, 0.35488406, 0.35628849, 0.35657422,\n",
       "         0.35659436, 0.3572505 , 0.35744955, 0.35771948, 0.35984693,\n",
       "         0.36048784, 0.36196278, 0.36275336, 0.36283389, 0.36418893,\n",
       "         0.36486851, 0.36609577, 0.36745751, 0.36793293, 0.3702077 ,\n",
       "         0.37086808, 0.37149843, 0.3716099 , 0.374699  , 0.37473092,\n",
       "         0.37560668, 0.37560859, 0.37650652, 0.37685689, 0.37687393,\n",
       "         0.37730591, 0.37746792, 0.37805227, 0.37878715, 0.38083367,\n",
       "         0.38111481, 0.38370495, 0.3839718 , 0.38430421, 0.38460363,\n",
       "         0.38588602, 0.38630709, 0.38712326, 0.38718397, 0.38762309,\n",
       "         0.38829798, 0.38840093, 0.3885686 , 0.38856879, 0.39023399,\n",
       "         0.39033698, 0.39069614, 0.39109126, 0.39128446, 0.39187246,\n",
       "         0.39190872, 0.39228633, 0.39358997, 0.39437254, 0.39458804,\n",
       "         0.39636976, 0.39680183, 0.39756059, 0.39901178, 0.40016896,\n",
       "         0.40081717, 0.40096196, 0.40232231, 0.4024518 , 0.40287023,\n",
       "         0.4035803 , 0.40442388, 0.40459006, 0.40481436, 0.40487577,\n",
       "         0.40612094, 0.4061661 , 0.40626708, 0.40721297, 0.4073541 ,\n",
       "         0.40750999, 0.40908712, 0.40939573, 0.40949772, 0.40975009,\n",
       "         0.40979694, 0.41052291, 0.41055575, 0.41115652, 0.41128785,\n",
       "         0.41164755, 0.41209993, 0.41223521, 0.41320582, 0.41401283,\n",
       "         0.4145701 , 0.41495533, 0.41624124, 0.41625342, 0.41865946,\n",
       "         0.42133893, 0.4223952 , 0.422458  , 0.4228709 , 0.42447547,\n",
       "         0.42517494, 0.42548066, 0.42550896, 0.42674578, 0.4268933 ,\n",
       "         0.4290278 , 0.42909806, 0.4315165 , 0.43212533, 0.4332209 ,\n",
       "         0.43362382, 0.43362751, 0.43366286, 0.43378434, 0.4343805 ,\n",
       "         0.43571488, 0.43600239, 0.4360414 , 0.43732352, 0.43927575,\n",
       "         0.43933629, 0.44014551, 0.44058902, 0.44094263, 0.44150682,\n",
       "         0.44174016, 0.4418191 , 0.44251222, 0.44332821, 0.44564037,\n",
       "         0.44641846, 0.44662538, 0.44689772, 0.45049182, 0.45073512,\n",
       "         0.45107258, 0.4516509 , 0.45184689, 0.45254007, 0.45432183,\n",
       "         0.45596603, 0.45680775, 0.45775136, 0.46043905, 0.46048534,\n",
       "         0.46123687, 0.46306548, 0.46324847, 0.46359586, 0.4638955 ,\n",
       "         0.46517788, 0.46547664, 0.46724196, 0.46803847, 0.46813465,\n",
       "         0.46855113, 0.46930704, 0.4701352 , 0.47192927, 0.47357258,\n",
       "         0.47504533, 0.4760241 , 0.47662546, 0.47712759, 0.47735016,\n",
       "         0.47891633, 0.47927652, 0.47935098, 0.47948615, 0.48149469,\n",
       "         0.48340368, 0.48389572, 0.48938171, 0.48945449, 0.49015793,\n",
       "         0.49228486, 0.49259369, 0.49323845, 0.49480704, 0.49613367,\n",
       "         0.4972729 , 0.49973107, 0.50212446, 0.50307509, 0.5031144 ,\n",
       "         0.50513419, 0.50952676, 0.5105026 , 0.51065256, 0.51083487,\n",
       "         0.51089011, 0.51214068, 0.51460495, 0.51596314, 0.51636946,\n",
       "         0.51667607, 0.51754077, 0.52067539, 0.52123449, 0.5217536 ,\n",
       "         0.52222978, 0.52340386, 0.5253794 , 0.52613405, 0.52693524,\n",
       "         0.5269507 , 0.52726301, 0.52731329, 0.52915728, 0.53024586,\n",
       "         0.53029898, 0.5304819 , 0.53054176, 0.53078923, 0.53085024,\n",
       "         0.53096252, 0.53098966, 0.53281872, 0.53314483, 0.53524669,\n",
       "         0.53711956, 0.53719192, 0.53981053, 0.54009699, 0.54014546,\n",
       "         0.54043747, 0.5460977 , 0.5461468 , 0.54774373, 0.54973305,\n",
       "         0.55026476, 0.55266064, 0.55404911, 0.55420633, 0.55510864,\n",
       "         0.55767464, 0.56193618, 0.56300167, 0.56384186, 0.56492231,\n",
       "         0.56697426, 0.56754977, 0.5679838 , 0.5688636 , 0.5709718 ,\n",
       "         0.57253234, 0.57326071, 0.57395015, 0.5766819 , 0.58195886,\n",
       "         0.58467749, 0.58517333, 0.58556883, 0.58704092, 0.58847259,\n",
       "         0.59052655, 0.59144535, 0.59305899, 0.59588356, 0.59948129,\n",
       "         0.60169191, 0.608802  , 0.61185816, 0.61599478, 0.61863729,\n",
       "         0.61948407, 0.62052972, 0.62845577, 0.62991067, 0.63707565,\n",
       "         0.63837165, 0.64555837, 0.64638224, 0.64638699, 0.6468311 ,\n",
       "         0.64940689, 0.64989112, 0.65622346, 0.66051134, 0.66133504,\n",
       "         0.66383522, 0.66488273, 0.66679883, 0.67954329, 0.68531346,\n",
       "         0.68726525, 0.69134621, 0.69249784, 0.69645921, 0.70729527,\n",
       "         0.70880755, 0.71339999, 0.71918242, 0.76980089, 0.77770161,\n",
       "         0.82435204, 0.83162446, 0.83845887, 0.86412947, 0.89364974])),\n",
       " (1.012082946069775, -0.0007871611788175525, 0.9994539309682382))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(data, dist='beta',sparams=(2,5), plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([34., 25., 34., 31., 25., 30., 36., 34., 33., 38., 37., 24., 42.,\n",
       "        50., 38., 30., 25., 23., 37., 31., 37., 32., 32., 44., 25., 23.,\n",
       "        41., 31., 37., 41.]),\n",
       " array([5.50178231e-03, 3.38647697e-01, 6.71793612e-01, 1.00493953e+00,\n",
       "        1.33808544e+00, 1.67123136e+00, 2.00437727e+00, 2.33752319e+00,\n",
       "        2.67066910e+00, 3.00381502e+00, 3.33696093e+00, 3.67010685e+00,\n",
       "        4.00325276e+00, 4.33639868e+00, 4.66954459e+00, 5.00269050e+00,\n",
       "        5.33583642e+00, 5.66898233e+00, 6.00212825e+00, 6.33527416e+00,\n",
       "        6.66842008e+00, 7.00156599e+00, 7.33471191e+00, 7.66785782e+00,\n",
       "        8.00100374e+00, 8.33414965e+00, 8.66729557e+00, 9.00044148e+00,\n",
       "        9.33358740e+00, 9.66673331e+00, 9.99987923e+00]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# uniform distribution\n",
    "\n",
    "data = np.random.uniform(low=0, high=10, size=1000)\n",
    "\n",
    "plt.hist(data, bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# t-test\n",
    "\n",
    "store_a_sales = np.random.normal(30000, 5000, 100)\n",
    "store_b_sales = np.random.normal(35000, 5000, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "t_stat, p_value = ttest_ind(store_a_sales, store_b_sales, equal_var=True, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5854665468241914e-10\n"
     ]
    }
   ],
   "source": [
    "print(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.8759207496273274e-09\n"
     ]
    }
   ],
   "source": [
    "# mann whitney\n",
    "from scipy.stats import mannwhitneyu\n",
    "\n",
    "u_stat, p_value = mannwhitneyu(store_a_sales, store_b_sales, alternative='less')\n",
    "\n",
    "print(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import data\n",
    "df = pd.read_csv('https://raw.githubusercontent.com/delinai/schulich_ds1_2024/main/Datasets/class_5_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Transaction_Category</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Electronics</td>\n",
       "      <td>93.775039</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>65.573266</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>61.982719</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Electronics</td>\n",
       "      <td>46.487828</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>93.138071</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Customer_ID  Age Gender  Campaign_Exposure  \\\n",
       "0           0            1   39   Male                  1   \n",
       "1           1            1   39   Male                  1   \n",
       "2           2            1   39   Male                  1   \n",
       "3           3            1   39   Male                  1   \n",
       "4           4            1   39   Male                  1   \n",
       "\n",
       "  Transaction_Category  Purchase_Amount  Premium_Product  \n",
       "0          Electronics        93.775039                0  \n",
       "1      Home Essentials        65.573266                0  \n",
       "2      Home Essentials        61.982719                0  \n",
       "3          Electronics        46.487828                1  \n",
       "4      Home Essentials        93.138071                0  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.drop('Unnamed: 0', axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Transaction_Category</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Electronics</td>\n",
       "      <td>93.775039</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>65.573266</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>61.982719</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Electronics</td>\n",
       "      <td>46.487828</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>Male</td>\n",
       "      <td>1</td>\n",
       "      <td>Home Essentials</td>\n",
       "      <td>93.138071</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Customer_ID  Age Gender  Campaign_Exposure Transaction_Category  \\\n",
       "0            1   39   Male                  1          Electronics   \n",
       "1            1   39   Male                  1      Home Essentials   \n",
       "2            1   39   Male                  1      Home Essentials   \n",
       "3            1   39   Male                  1          Electronics   \n",
       "4            1   39   Male                  1      Home Essentials   \n",
       "\n",
       "   Purchase_Amount  Premium_Product  \n",
       "0        93.775039                0  \n",
       "1        65.573266                0  \n",
       "2        61.982719                0  \n",
       "3        46.487828                1  \n",
       "4        93.138071                0  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10034 entries, 0 to 10033\n",
      "Data columns (total 7 columns):\n",
      " #   Column                Non-Null Count  Dtype  \n",
      "---  ------                --------------  -----  \n",
      " 0   Customer_ID           10034 non-null  int64  \n",
      " 1   Age                   10034 non-null  int64  \n",
      " 2   Gender                10034 non-null  object \n",
      " 3   Campaign_Exposure     10034 non-null  int64  \n",
      " 4   Transaction_Category  10034 non-null  object \n",
      " 5   Purchase_Amount       10034 non-null  float64\n",
      " 6   Premium_Product       10034 non-null  int64  \n",
      "dtypes: float64(1), int64(4), object(2)\n",
      "memory usage: 548.9+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10034.000000</td>\n",
       "      <td>10034.000000</td>\n",
       "      <td>10034.000000</td>\n",
       "      <td>10034.000000</td>\n",
       "      <td>10034.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>499.098366</td>\n",
       "      <td>34.550827</td>\n",
       "      <td>0.624277</td>\n",
       "      <td>55.894060</td>\n",
       "      <td>0.269085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>290.841403</td>\n",
       "      <td>9.838315</td>\n",
       "      <td>0.484333</td>\n",
       "      <td>22.738743</td>\n",
       "      <td>0.443506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-37.297202</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>247.250000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>40.241688</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>497.000000</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>55.494446</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>752.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>70.915768</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>139.624489</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Customer_ID           Age  Campaign_Exposure  Purchase_Amount  \\\n",
       "count  10034.000000  10034.000000       10034.000000     10034.000000   \n",
       "mean     499.098366     34.550827           0.624277        55.894060   \n",
       "std      290.841403      9.838315           0.484333        22.738743   \n",
       "min        1.000000      2.000000           0.000000       -37.297202   \n",
       "25%      247.250000     28.000000           0.000000        40.241688   \n",
       "50%      497.000000     35.000000           1.000000        55.494446   \n",
       "75%      752.000000     41.000000           1.000000        70.915768   \n",
       "max     1000.000000     73.000000           1.000000       139.624489   \n",
       "\n",
       "       Premium_Product  \n",
       "count     10034.000000  \n",
       "mean          0.269085  \n",
       "std           0.443506  \n",
       "min           0.000000  \n",
       "25%           0.000000  \n",
       "50%           0.000000  \n",
       "75%           1.000000  \n",
       "max           1.000000  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.rename(columns = {'Age':'Customer_Age_Months'}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_Age_Months</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Transaction_Category</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Customer_ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Customer_Age_Months  Gender  Campaign_Exposure  \\\n",
       "Customer_ID                                                   \n",
       "1                              1       1                  1   \n",
       "2                              1       1                  1   \n",
       "3                              1       1                  1   \n",
       "4                              1       1                  1   \n",
       "5                              1       1                  1   \n",
       "...                          ...     ...                ...   \n",
       "996                            1       1                  1   \n",
       "997                            1       1                  1   \n",
       "998                            1       1                  1   \n",
       "999                            1       1                  1   \n",
       "1000                           1       1                  1   \n",
       "\n",
       "             Transaction_Category  Purchase_Amount  Premium_Product  \n",
       "Customer_ID                                                          \n",
       "1                               3               15                2  \n",
       "2                               3                9                2  \n",
       "3                               2                5                2  \n",
       "4                               3                7                2  \n",
       "5                               3               15                2  \n",
       "...                           ...              ...              ...  \n",
       "996                             3               12                2  \n",
       "997                             3               15                2  \n",
       "998                             3               10                2  \n",
       "999                             3                7                2  \n",
       "1000                            3               14                2  \n",
       "\n",
       "[1000 rows x 6 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('Customer_ID').nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Purchase_Amount'>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(df['Purchase_Amount'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Customer_ID', 'Customer_Age_Months', 'Gender', 'Campaign_Exposure',\n",
       "       'Transaction_Category', 'Purchase_Amount', 'Premium_Product'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "cust_level = df.groupby('Customer_ID')[['Customer_Age_Months', 'Gender', 'Campaign_Exposure',\n",
    "       'Transaction_Category', 'Purchase_Amount', 'Premium_Product']].agg({'Customer_Age_Months':'max', 'Campaign_Exposure':'max', \n",
    "                                                                          'Purchase_Amount':'mean', 'Premium_Product':'mean'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_Age_Months</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Customer_ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39</td>\n",
       "      <td>1</td>\n",
       "      <td>62.740377</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>49.089058</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>50.121352</td>\n",
       "      <td>0.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>50</td>\n",
       "      <td>0</td>\n",
       "      <td>61.712429</td>\n",
       "      <td>0.285714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>58.347321</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>58.144164</td>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>52</td>\n",
       "      <td>1</td>\n",
       "      <td>61.809425</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>43.168841</td>\n",
       "      <td>0.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>60.017800</td>\n",
       "      <td>0.285714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>70.610554</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Customer_Age_Months  Campaign_Exposure  Purchase_Amount  \\\n",
       "Customer_ID                                                            \n",
       "1                             39                  1        62.740377   \n",
       "2                             33                  0        49.089058   \n",
       "3                             41                  0        50.121352   \n",
       "4                             50                  0        61.712429   \n",
       "5                             32                  1        58.347321   \n",
       "...                          ...                ...              ...   \n",
       "996                           32                  1        58.144164   \n",
       "997                           52                  1        61.809425   \n",
       "998                           41                  0        43.168841   \n",
       "999                           29                  0        60.017800   \n",
       "1000                          40                  1        70.610554   \n",
       "\n",
       "             Premium_Product  \n",
       "Customer_ID                   \n",
       "1                   0.400000  \n",
       "2                   0.333333  \n",
       "3                   0.200000  \n",
       "4                   0.285714  \n",
       "5                   0.400000  \n",
       "...                      ...  \n",
       "996                 0.083333  \n",
       "997                 0.333333  \n",
       "998                 0.200000  \n",
       "999                 0.285714  \n",
       "1000                0.500000  \n",
       "\n",
       "[1000 rows x 4 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cust_level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "campaign_cx = cust_level[cust_level['Campaign_Exposure']==1]\n",
    "reg_cx = cust_level[cust_level['Campaign_Exposure']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Campaign_Exposure', ylabel='Purchase_Amount'>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x = 'Campaign_Exposure', y = 'Purchase_Amount', data=cust_level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Campaign_Exposure', ylabel='Premium_Product'>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWIrf4WbNmjU6duxYm/Zjx45pzZo1XSoKAADAX36HmyuvvFL79+9v015fX68rr7yyS0UBAAD4y+9wYxiGbDZbm/Z//etf6tOnT5eKAgAA8Nd3OrvCj3/8Y0mSzWbT7bffLofD4V3W2tqqDRs26PLLL+/UNktLSzVv3jy53W6NGDFCCxYsUGpqart9lyxZotzcXJ82h8Oho0ePdvJIAACAFXU63ERFRUn66sxNZGSkwsLCvMtCQkI0cuRITZgwocPbW7lypVwulxYvXqy0tDSVlJQoMzNTW7ZsUf/+/dtdp2/fvtqyZYt3vr0zSAAA4PTU6XDz3HPPSZISExP1y1/+UuHh4V0qoLi4WBMmTPCejVm8eLFWrVqlsrIyTZs2rd11bDabYmNju7RfAABgTX6PucnJydHOnTvbtH/yySfatm1bh7bR3NysmpoaZWRk/Lsgu10ZGRmqqqo64XqHDh1SQkKC4uPjdeONN2rjxo0n7NvU1KSGhgafCQAAWJff4eb222/Xe++916b9b3/7m26//fYObWPfvn1qbW2V0+n0aXc6nXK73e2uM2TIEJWVlel///d/tXz5cnk8Hl1++eX64osv2u1fVFSkqKgo7xQfH9+h2gAAQO/kd7j54IMPNGrUqDbtI0eO1Pr167tS00mlp6crJydHSUlJGjNmjF555RWdddZZevLJJ9vtn5+fr/r6eu+0Y8eOU1YbAAAwX6fH3Bxns9l08ODBNu319fVqbW3t0DZiYmIUFBSkuro6n/a6uroOj6kJDg7WpZdeqk8//bTd5Q6Hw+eOLgAAYG1+n7kZPXq0ioqKfIJMa2urioqK9L3vfa9D2wgJCVFycrIqKiq8bR6PRxUVFUpPT+/QNlpbW/WPf/xDAwYM6NwBAAAAS/L7zM3cuXM1evRoDRkyRP/xH/8hSXrnnXfU0NCgt956q8PbcblcGj9+vFJSUpSamqqSkhI1NjZ6757KyclRXFycioqKJEkPPfSQRo4cqfPPP18HDhzQvHnztH37dt15553+HgoAALAQv8PN0KFDtWHDBj3xxBP68MMPFRYWppycHOXl5Sk6OrrD28nKytLevXs1c+ZMud1uJSUlqby83DvIuLa2Vnb7v08wffnll5owYYLcbrfOOOMMJScn67333tPQoUP9PRQAAGAhfocbSTr77LM1Z86cLheRl5envLy8dpdVVlb6zD/++ON6/PHHu7xPAABgTX6Hm2978/fo0aP93TQAAIDf/A43V1xxRZu2r78GoaN3TAEAAASS33dLffnllz7Tnj17VF5erssuu0xvvPFGIGsEAADoML/P3Bx/gebXXX311QoJCZHL5VJNTU2XCgMAAPCH32duTsTpdPq8sRsAAKA7+X3mZsOGDT7zhmFo9+7deuSRR5SUlNTVugAAAPzid7hJSkqSzWaTYRg+7SNHjlRZWVmXCwMAAPCH3+Fm69atPvN2u11nnXWWQkNDu1wUAACAv/wONwkJCYGsAwAAICA6FW7mz5/f4b5TpkzpdDEAAABd1alw883XHuzdu1eHDx9Wv379JEkHDhxQeHi4+vfvT7gBAACm6NSt4Fu3bvVOhYWFSkpK0qZNm7R//37t379fmzZt0ne/+109/PDDp6peAACAk/L7OTcPPPCAFixYoCFDhnjbhgwZoscff1wzZswISHEAAACd5Xe42b17t44dO9amvbW1VXV1dV0qCgAAwF9+h5urrrpKEydO1Lp167xtNTU1uueee5SRkRGQ4gAAADrL73BTVlam2NhYpaSkyOFwyOFwKDU1VU6nU88880wgawQAAOgwv59zc9ZZZ2n16tX6+OOPtWnTJtlsNl144YUaPHhwIOsDAADoFL/DzXGDBw/WBRdcIEmy2WxdLggAAKAruvRW8Oeff17Dhg1TWFiYwsLCNHz4cC1btixQtQEAAHSa32duiouL9cADDygvL0+jRo2SJL377ru6++67tW/fPt13330BKxIAAKCj/A43CxYs0KJFi5STk+Ntu+GGG3TxxRfrwQcfJNwAAABTdOk5N5dffnmb9ssvv1y7d+/uUlEAAAD+8jvcnH/++fqf//mfNu0rV670DjAGAADobn5flpo1a5aysrK0Zs0a75ibtWvXqqKiot3QAwAA0B38PnNz0003qbq6WjExMXr11Vf16quvKiYmRtXV1frRj34UyBoBAAA6zK8zNy0tLZo4caIeeOABLV++PNA1AQAA+M2vMzfBwcF6+eWXA10LAABAl/l9WWrs2LF69dVXA1gKAABA1/k9oPiCCy7QQw89pLVr1yo5OVl9+vTxWT5lypQuFwcAANBZfoebZ599Vv369VNNTY1qamp8ltlsNsINAAAwhd/hZuvWrYGsAwAAICD8Cjd//etf9cc//lHNzc266qqrdM011wS6LgAAAL90Oty89NJLysrKUlhYmIKDg1VcXKy5c+fq/vvvPxX1AQAAdEqn75YqKirShAkTVF9fry+//FKzZ8/WnDlzulREaWmpEhMTFRoaqrS0NFVXV3dovRdeeEE2m01jx47t0v4BAIB1dDrcbNmyRffff7+CgoIkSb/4xS908OBB7dmzx68CVq5cKZfLpYKCAq1bt04jRoxQZmbmt25v27Ztuv/++/Uf//Effu0XAABYU6fDzeHDh9W3b1/vfEhIiEJDQ3Xo0CG/CiguLtaECROUm5uroUOHavHixQoPD1dZWdkJ12ltbVV2drZmzZqlQYMG+bVfAABgTX4NKH7mmWcUERHhnT927JiWLFmimJgYb1tHbgVvbm5WTU2N8vPzvW12u10ZGRmqqqo64XoPPfSQ+vfvrzvuuEPvvPPOSffR1NSkpqYm73xDQ8O31gUAJ1NXV6f6+nqzyzjtbd++3edPmC8qKkpOp9PsMjofbgYOHKinn37apy02NlbLli3zznf0OTf79u1Ta2trmw/C6XRq8+bN7a7z7rvv6tlnn9X69es7VG9RUZFmzZrVob4A8G3q6ur0s9ty1NLc9O2d0S0KCwvNLgH/X3CIQ8uXPW96wOl0uNm2bdspKKNjDh48qNtuu01PP/20z1mik8nPz5fL5fLONzQ0KD4+/lSVCMDi6uvr1dLcpCODxsgTGmV2OUCPYT9aL33+F9XX1/e+cNNZw4YN0+rVq9sNFDExMQoKClJdXZ1Pe11dnWJjY9v0/+yzz7Rt2zZdf/313jaPxyNJ+s53vqMtW7bovPPO81nH4XDI4XAE4lAAwMsTGiVPn479kgWge/n94syO2rZtm1paWtpdFhISouTkZFVUVHjbPB6PKioqlJ6e3qb/hRdeqH/84x9av369d7rhhht05ZVXav369ZyRAQAAp/7MzbdxuVwaP368UlJSlJqaqpKSEjU2Nio3N1eSlJOTo7i4OBUVFSk0NFSXXHKJz/r9+vWTpDbtAADg9GR6uMnKytLevXs1c+ZMud1uJSUlqby83Hu9rra2Vnb7KT/BBAAALML0cCNJeXl5ysvLa3dZZWXlSdddsmRJ4AsCAAC9FqdEAACApRBuAACApZzycPPkk0+afr87AAA4fXRpzM3777+vt99+W3v27PE+b+a44uJiSdK4ceO6sgsAAIBO8TvczJkzRzNmzNCQIUPkdDpls9m8y77+dwAAgO7kd7j57W9/q7KyMt1+++0BLAcAAKBr/B5zY7fbNWrUqEDWAgAA0GV+h5v77rtPpaWlgawFAACgy/y+LHX//ffruuuu03nnnaehQ4cqODjYZ/krr7zS5eIAAAA6y+9wM2XKFL399tu68sordeaZZzKIGAAA9Ah+h5ulS5fq5Zdf1nXXXRfIegAAALrE7zE30dHROu+88wJZCwAAQJf5HW4efPBBFRQU6PDhw4GsBwAAoEv8viw1f/58ffbZZ3I6nUpMTGwzoHjdunVdLg4AAKCz/A43Y8eODWAZAAAAgeF3uCkoKAhkHQAAAAFxyt8KDgAA0J38PnNjt9tP+myb1tZWfzcNAADgN7/DzR/+8Aef+ZaWFn3wwQdaunSpZs2a1eXCAAAA/OF3uLnxxhvbtN188826+OKLtXLlSt1xxx1dKgwAAMAfAR9zM3LkSFVUVAR6swAAAB0S0HBz5MgRzZ8/X3FxcYHcLAAAQIf5fVnqjDPO8BlQbBiGDh48qPDwcC1fvjwgxQEAAHSW3+Hm8ccf9wk3drtdZ511ltLS0nTGGWcEpDgAAIDO8jvc3H777QEsAwAAIDA6FW42bNigSy65RHa7XRs2bDhp3+HDh3epMAAAAH90KtwkJSXJ7Xarf//+SkpKks1mk2EYbfrZbDYe4gcAAEzRqXCzdetWnXXWWd6/AwAA9DSdCjcJCQnt/h0AAKCn8HtAsSTt2rVL7777rvbs2SOPx+OzbMqUKV0qDAAAwB9+h5slS5Zo4sSJCgkJ0ZlnnulzW7jNZiPcAAAAU/gdbh544AHNnDlT+fn5stsD/hYHAAAAv/idSg4fPqxbb701IMGmtLRUiYmJCg0NVVpamqqrq0/Y95VXXlFKSor69eunPn36KCkpScuWLetyDQAAwBr8TiZ33HGHXnzxxS4XsHLlSrlcLhUUFGjdunUaMWKEMjMztWfPnnb7R0dHa/r06aqqqtKGDRuUm5ur3Nxcvf76612uBQAA9H5+X5YqKirSD3/4Q5WXl2vYsGEKDg72WV5cXNyh7RQXF2vChAnKzc2VJC1evFirVq1SWVmZpk2b1qb/FVdc4TM/depULV26VO+++64yMzP9OxgAAGAZXQo3r7/+uoYMGSJJbQYUd0Rzc7NqamqUn5/vbbPb7crIyFBVVdW3rm8Yht566y1t2bJFc+fO7eQRAAAAK/I73Dz22GMqKyvr0jum9u3bp9bWVjmdTp92p9OpzZs3n3C9+vp6xcXFqampSUFBQVq4cKGuvvrqdvs2NTWpqanJO9/Q0OB3vZ1RV1en+vr6btkXTmz79u0+f8J8UVFRbb7zvZH9yAGzSwB6lJ70nfA73DgcDo0aNSqQtXRYZGSk1q9fr0OHDqmiokIul0uDBg1qc8lK+uoM06xZs7q1vrq6Ov3sthy1NDd9e2d0i8LCQrNLwP8XHOLQ8mXP9/qAE7Z1jdklADgBv8PN1KlTtWDBAs2fP9/vncfExCgoKEh1dXU+7XV1dYqNjT3hena7Xeeff76kr953tWnTJhUVFbUbbvLz8+VyubzzDQ0Nio+P97vmjqivr1dLc5OODBojT2jUKd0X0JvYj9ZLn/9F9fX1vT7cHDl3tDxh/cwuA+gx7EcO9JjQ73e4qa6u1ltvvaXXXntNF198cZsBxa+88sq3biMkJETJycmqqKjQ2LFjJUkej0cVFRXKy8vrcC0ej8fn0tPXORwOORyODm8rkDyhUfL0iTFl3wBOLU9YP77fQA/ld7jp16+ffvzjH3e5AJfLpfHjxyslJUWpqakqKSlRY2Oj9+6pnJwcxcXFqaioSNJXl5lSUlJ03nnnqampSatXr9ayZcu0aNGiLtcCAAB6P7/DzXPPPReQArKysrR3717NnDlTbrdbSUlJKi8v956yrq2t9XlQYGNjoyZNmqQvvvhCYWFhuvDCC7V8+XJlZWUFpB4AANC7denFmceOHVNlZaU+++wzjRs3TpGRkdq1a5f69u2riIiIDm8nLy/vhJehKisrfeZnz56t2bNnd6VsAABgYX6Hm+3bt+uaa65RbW2tmpqadPXVVysyMlJz585VU1OTFi9eHMg6AQAAOsTv1y9MnTpVKSkp+vLLLxUWFuZt/9GPfqSKioqAFAcAANBZfp+5eeedd/Tee+8pJCTEpz0xMVE7d+7scmEAAAD+8PvMjcfjUWtra5v2L774QpGRkV0qCgAAwF9+h5vvf//7Kikp8c7bbDYdOnRIBQUF+sEPfhCI2gAAADrN78tSjz76qK655hoNHTpUR48e1bhx4/TJJ58oJiZGv//97wNZIwAAQIf5HW7i4+P14YcfauXKlfrwww916NAh3XHHHcrOzvYZYAwAANCd/Ao3LS0tuvDCC/Xaa68pOztb2dnZga4LAADAL36NuQkODtbRo0cDXQsAAECX+T2gePLkyZo7d66OHTsWyHoAAAC6xO8xN++//74qKir0xhtvaNiwYerTp4/P8o68FRwAACDQuvRW8JtuuimQtQAAAHRZp8ONx+PRvHnz9PHHH6u5uVn/+Z//qQcffJA7pAAAQI/Q6TE3hYWF+vWvf62IiAjFxcVp/vz5mjx58qmoDQAAoNM6HW6ef/55LVy4UK+//rpeffVV/fGPf9SKFSvk8XhORX0AAACd0ulwU1tb6/N6hYyMDNlsNu3atSughQEAAPij0+Hm2LFjCg0N9WkLDg5WS0tLwIoCAADwV6cHFBuGodtvv10Oh8PbdvToUd19990+t4NzKzgAADBDp8PN+PHj27T97Gc/C0gxAAAAXdXpcPPcc8+dijoAAAACwu/XLwAAAPREhBsAAGAphBsAAGAphBsAAGAphBsAAGAphBsAAGAphBsAAGAphBsAAGAphBsAAGAphBsAAGApnX79AgBAsh+tN7sEoEfpSd8Jwg0AdEJUVJSCQxzS538xuxSgxwkOcSgqKsrsMgg3ANAZTqdTy5c9r/r6nvNb6ulq+/btKiws1PTp05WQkGB2OdBX4d/pdJpdRs8IN6WlpZo3b57cbrdGjBihBQsWKDU1td2+Tz/9tJ5//nl99NFHkqTk5GTNmTPnhP0BINCcTmeP+A8cX0lISNDgwYPNLgM9iOkDileuXCmXy6WCggKtW7dOI0aMUGZmpvbs2dNu/8rKSv30pz/V22+/raqqKsXHx+v73/++du7c2c2VAwCAnsj0cFNcXKwJEyYoNzdXQ4cO1eLFixUeHq6ysrJ2+69YsUKTJk1SUlKSLrzwQj3zzDPyeDyqqKjo5soBAEBPZOplqebmZtXU1Cg/P9/bZrfblZGRoaqqqg5t4/Dhw2ppaVF0dHS7y5uamtTU1OSdb2ho6FrRnWA/cqDb9gX0BnwnAHQHU8PNvn371Nra2ubatdPp1ObNmzu0jV/96lc6++yzlZGR0e7yoqIizZo1q8u1+iNs6xpT9gsAwOmsRwwo9tcjjzyiF154QZWVlQoNDW23T35+vlwul3e+oaFB8fHx3VLfkXNHyxPWr1v2BfQG9iMHCP0ATjlTw01MTIyCgoJUV1fn015XV6fY2NiTrvvoo4/qkUce0Z///GcNHz78hP0cDoccDkdA6u0sT1g/efrEmLJvAABOV6YOKA4JCVFycrLPYODjg4PT09NPuN5vfvMbPfzwwyovL1dKSkp3lAoAAHoJ0y9LuVwujR8/XikpKUpNTVVJSYkaGxuVm5srScrJyVFcXJyKiookSXPnztXMmTP1u9/9TomJiXK73ZKkiIgIRUREmHYcAACgZzA93GRlZWnv3r2aOXOm3G63kpKSVF5e7h1kXFtbK7v93yeYFi1apObmZt18880+2ykoKNCDDz7YnaUDAIAeyPRwI0l5eXnKy8trd1llZaXP/LZt2059QQAAoNcy/SF+AAAAgUS4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAltIjwk1paakSExMVGhqqtLQ0VVdXn7Dvxo0bddNNNykxMVE2m00lJSXdVygAAOjxTA83K1eulMvlUkFBgdatW6cRI0YoMzNTe/bsabf/4cOHNWjQID3yyCOKjY3t5moBAEBPZ3q4KS4u1oQJE5Sbm6uhQ4dq8eLFCg8PV1lZWbv9L7vsMs2bN0+33nqrHA5HN1cLAAB6uu+YufPm5mbV1NQoPz/f22a325WRkaGqqqqA7KOpqUlNTU3e+YaGhoBstyPsR+u7bV9Ab8B3AkB3MDXc7Nu3T62trXI6nT7tTqdTmzdvDsg+ioqKNGvWrIBsq6OioqIUHOKQPv9Lt+4X6A2CQxyKiooyuwwAFmZquOkO+fn5crlc3vmGhgbFx8ef0n06nU4tX/a86uv5LdVs27dvV2FhoaZPn66EhASzy4G+Cv/f/IUGAALJ1HATExOjoKAg1dXV+bTX1dUFbLCww+EwZWyO0+nkP/AeJCEhQYMHDza7DABANzB1QHFISIiSk5NVUVHhbfN4PKqoqFB6erqJlQEAgN7K9MtSLpdL48ePV0pKilJTU1VSUqLGxkbl5uZKknJychQXF6eioiJJXw1C/uc//+n9+86dO7V+/XpFRETo/PPPN+04AABAz2B6uMnKytLevXs1c+ZMud1uJSUlqby83HtJp7a2Vnb7v08w7dq1S5deeql3/tFHH9Wjjz6qMWPGqLKysrvLBwAAPYzp4UaS8vLylJeX1+6ybwaWxMREGYbRDVUBAIDeyPSH+AEAAAQS4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFhKjwg3paWlSkxMVGhoqNLS0lRdXX3S/i+++KIuvPBChYaGatiwYVq9enU3VQoAAHo608PNypUr5XK5VFBQoHXr1mnEiBHKzMzUnj172u3/3nvv6ac//anuuOMOffDBBxo7dqzGjh2rjz76qJsrBwAAPZHp4aa4uFgTJkxQbm6uhg4dqsWLFys8PFxlZWXt9v/tb3+ra665Rr/85S910UUX6eGHH9Z3v/tdPfHEE91cOQAA6IlMDTfNzc2qqalRRkaGt81utysjI0NVVVXtrlNVVeXTX5IyMzNP2B8AAJxevmPmzvft26fW1lY5nU6fdqfTqc2bN7e7jtvtbre/2+1ut39TU5Oampq88w0NDV2s+vRx9OhR1dbWml1Gl2zfvt3nz95u4MCBCg0NNbsMWADf756H73fgmBpuukNRUZFmzZpldhm9Um1tre666y6zywiIwsJCs0sIiKeeekqDBw82uwxYAN/vnofvd+CYGm5iYmIUFBSkuro6n/a6ujrFxsa2u05sbGyn+ufn58vlcnnnGxoaFB8f38XKTw8DBw7UU089ZXYZ+JqBAweaXQIsgu93z8P3O3BMDTchISFKTk5WRUWFxo4dK0nyeDyqqKhQXl5eu+ukp6eroqJCP//5z71tb775ptLT09vt73A45HA4Al36aSE0NJTfIgCL4vsNKzP9spTL5dL48eOVkpKi1NRUlZSUqLGxUbm5uZKknJwcxcXFqaioSJI0depUjRkzRo899piuu+46vfDCC/r73//ObyAAAEBSDwg3WVlZ2rt3r2bOnCm3262kpCSVl5d7Bw3X1tbKbv/3TV2XX365fve732nGjBn69a9/rQsuuECvvvqqLrnkErMOAQAA9CA2wzAMs4voTg0NDYqKilJ9fb369u1rdjkAAKADOvPz2/SH+AEAAAQS4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFiK6e+W6m7H3zbR0NBgciUAAKCjjv/c7shbo067cHPw4EFJUnx8vMmVAACAzjp48KCioqJO2ue0e3Gmx+PRrl27FBkZKZvNZnY5OMUaGhoUHx+vHTt28KJUwGL4fp9eDMPQwYMHdfbZZ8tuP/momtPuzI3dbtc555xjdhnoZn379uU/P8Ci+H6fPr7tjM1xDCgGAACWQrgBAACWQriBpTkcDhUUFMjhcJhdCoAA4/uNEzntBhQDAABr48wNAACwFMINAACwFMINAACwFMINLK20tFSJiYkKDQ1VWlqaqqurzS4JQACsWbNG119/vc4++2zZbDa9+uqrZpeEHoRwA8tauXKlXC6XCgoKtG7dOo0YMUKZmZnas2eP2aUB6KLGxkaNGDFCpaWlZpeCHoi7pWBZaWlpuuyyy/TEE09I+urVG/Hx8br33ns1bdo0k6sDECg2m01/+MMfNHbsWLNLQQ/BmRtYUnNzs2pqapSRkeFts9vtysjIUFVVlYmVAQBONcINLGnfvn1qbW2V0+n0aXc6nXK73SZVBQDoDoQbAABgKYQbWFJMTIyCgoJUV1fn015XV6fY2FiTqgIAdAfCDSwpJCREycnJqqio8LZ5PB5VVFQoPT3dxMoAAKfad8wuADhVXC6Xxo8fr5SUFKWmpqqkpESNjY3Kzc01uzQAXXTo0CF9+umn3vmtW7dq/fr1io6O1sCBA02sDD0Bt4LD0p544gnNmzdPbrdbSUlJmj9/vtLS0swuC0AXVVZW6sorr2zTPn78eC1ZsqT7C0KPQrgBAACWwpgbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAKZZsmSJ+vXrZ3YZACyGcAP0cm63W/fee68GDRokh8Oh+Ph4XX/99T4vDe2psrKy9PHHH3frPq+44grZbLY20913392tdQA4dXhxJtCLbdu2TaNGjVK/fv00b948DRs2TC0tLXr99dc1efJkbd682ewSTyosLExhYWHdvt8JEybooYce8mkLDw/v9joCqbm5WSEhIWaXAfQInLkBerFJkybJZrOpurpaN910kwYPHqyLL75YLpdLf/3rXyVJxcXFGjZsmPr06aP4+HhNmjRJhw4d8m7j+KWh1157TUOGDFF4eLhuvvlmHT58WEuXLlViYqLOOOMMTZkyRa2trd71EhMT9fDDD+unP/2p+vTpo7i4OJWWlvrU19F9f93s2bPVv39/RUZG6s4779S0adOUlJTkXX777bdr7NixevTRRzVgwACdeeaZmjx5slpaWjr8uYWHhys2NtZn6tu3ryTp+eefV0REhD755BOfz/nCCy/U4cOHO3zstbW1uvHGGxUREaG+ffvqJz/5ierq6rzLP/zwQ1155ZWKjIxU3759lZycrL///e+SpAcffNDnmCWppKREiYmJbT6HwsJCnX322RoyZIgkaceOHfrJT36ifv36KTo6WjfeeKO2bdvW4c8GsALCDdBL7d+/X+Xl5Zo8ebL69OnTZvnx0GC32zV//nxt3LhRS5cu1VtvvaX//u//9ul7+PBhzZ8/Xy+88ILKy8tVWVmpH/3oR1q9erVWr16tZcuW6cknn9RLL73ks968efM0YsQIffDBB5o2bZqmTp2qN99807u8I/v+uhUrVqiwsFBz585VTU2NBg4cqEWLFrXp9/bbb+uzzz7T22+/raVLl2rJkiUBexN0Tk6OfvCDHyg7O1vHjh3TqlWr9Mwzz2jFihU+Z3dOduwej0c33nij9u/fr7/85S9688039fnnnysrK8u7fnZ2ts455xy9//77qqmp0bRp0xQcHNypWisqKrRlyxa9+eabeu2119TS0qLMzExFRkbqnXfe0dq1axUREaFrrrlGzc3NAfl8gF7BANAr/e1vfzMkGa+88kqn1nvxxReNM8880zv/3HPPGZKMTz/91Ns2ceJEIzw83Dh48KC3LTMz05g4caJ3PiEhwbjmmmt8tp2VlWVce+21ndp3VFSUdz4tLc2YPHmyzzqjRo0yRowY4Z0fP368kZCQYBw7dszbdssttxhZWVknOep/GzNmjBEcHGz06dPHZ1q+fLm3z/79+41zzjnHuOeeewyn02kUFhb6bOPbjv2NN94wgoKCjNraWu/yjRs3GpKM6upqwzAMIzIy0liyZEm7NRYUFPgcs2EYxuOPP24kJCT4fA5Op9Noamryti1btswYMmSI4fF4vG1NTU1GWFiY8frrr3fg0wGsgTM3QC9lGEaH+v35z3/WVVddpbi4OEVGRuq2227Tv/71L+8lFumryzTnnXeed97pdCoxMVERERE+bXv27PHZdnp6epv5TZs2dWrfX7dlyxalpqb6tH1zXpIuvvhiBQUFeecHDBjQpraTyc7O1vr1632mG264wbv8jDPO0LPPPqtFixbpvPPO07Rp09ps42THvmnTJsXHxys+Pt67fOjQoerXr5+3j8vl0p133qmMjAw98sgj+uyzzzpc/3HDhg3zGWfz4Ycf6tNPP1VkZKQiIiIUERGh6OhoHT161K/tA70V4QbopS644ALZbLaTDhretm2bfvjDH2r48OF6+eWXVVNT4x0b8vXLFN+8HGKz2dpt83g8Ha6vo/v2R1dri4qK0vnnn+8zRUZG+vRZs2aNgoKCtHv3bjU2Nnap3vY8+OCD2rhxo6677jq99dZbGjp0qP7whz9I+upy3jfDa3tjir55OfLQoUNKTk5uE9w+/vhjjRs3LuDHAPRUhBugl4qOjlZmZqZKS0vb/eF74MAB1dTUyOPx6LHHHtPIkSM1ePBg7dq1K2A1HB+0/PX5iy66SJL82veQIUP0/vvv+7R9c747vPfee5o7d67++Mc/KiIiQnl5eW36nOzYL7roIu3YsUM7duzwLv/nP/+pAwcOaOjQod62wYMH67777tMbb7yhH//4x3ruueckSWeddZbcbrdPwFm/fv231v3d735Xn3zyifr3798mvEVFRXXqMwB6M8IN0IuVlpaqtbVVqampevnll/XJJ59o06ZNmj9/vtLT03X++eerpaVFCxYs0Oeff65ly5Zp8eLFAdv/2rVr9Zvf/EYff/yxSktL9eKLL2rq1KmS5Ne+7733Xj377LNaunSpPvnkE82ePVsbNmyQzWYLWM3SVwOo3W63z/Tll19Kkg4ePKjbbrtNU6ZM0bXXXqsVK1Zo5cqVbQZTn+zYMzIyNGzYMGVnZ2vdunWqrq5WTk6OxowZo5SUFB05ckR5eXmqrKzU9u3btXbtWr3//vvecHTFFVdo7969+s1vfqPPPvtMpaWl+tOf/vStx5Wdna2YmBjdeOONeuedd7R161ZVVlZqypQp+uKLLwL6GQI9msljfgB00a5du4zJkycbCQkJRkhIiBEXF2fccMMNxttvv20YhmEUFxcbAwYMMMLCwozMzEzj+eefNyQZX375pWEYbQf1Gkb7A1rHjx9v3Hjjjd75hIQEY9asWcYtt9xihIeHG7GxscZvf/tbn3X82fdDDz1kxMTEGBEREcZ//dd/GVOmTDFGjhx5wjoMwzCmTp1qjBkzpkOf15gxYwxJbabMzEzDMAwjNzfXGDZsmHH06FHvOo899pgRHR1tfPHFFx0+9u3btxs33HCD0adPHyMyMtK45ZZbDLfbbRjGV4N8b731ViM+Pt4ICQkxzj77bCMvL884cuSId/1FixYZ8fHxRp8+fYycnByjsLCwzYDib34OhmEYu3fvNnJycoyYmBjD4XAYgwYNMiZMmGDU19d36PMBrMBmGB0clQgAX5OYmKif//zn+vnPf35K93P11VcrNjZWy5YtO6X76YzuOnYA/uEJxQB6jMOHD2vx4sXKzMxUUFCQfv/73+vPf/6zz7NzAODbEG4A9Bg2m02rV69WYWGhjh49qiFDhujll19WRkZGh9Z/5513dO21155w+defjgzAurgsBcAyjhw5op07d55w+fnnn9+N1QAwC+EGAABYCreCAwAASyHcAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAAS/l/m+lmbO0LYUAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x = 'Campaign_Exposure', y = 'Premium_Product', data=cust_level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_Age_Months</th>\n",
       "      <th>Campaign_Exposure</th>\n",
       "      <th>Purchase_Amount</th>\n",
       "      <th>Premium_Product</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Customer_ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39</td>\n",
       "      <td>1</td>\n",
       "      <td>62.740377</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>58.347321</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>62.385110</td>\n",
       "      <td>0.153846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>57.681042</td>\n",
       "      <td>0.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>30</td>\n",
       "      <td>1</td>\n",
       "      <td>57.207082</td>\n",
       "      <td>0.214286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>61.435691</td>\n",
       "      <td>0.071429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
       "      <td>65.697122</td>\n",
       "      <td>0.363636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>58.144164</td>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>52</td>\n",
       "      <td>1</td>\n",
       "      <td>61.809425</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>70.610554</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Customer_Age_Months  Campaign_Exposure  Purchase_Amount  \\\n",
       "Customer_ID                                                            \n",
       "1                             39                  1        62.740377   \n",
       "5                             32                  1        58.347321   \n",
       "6                             32                  1        62.385110   \n",
       "10                            40                  1        57.681042   \n",
       "11                            30                  1        57.207082   \n",
       "...                          ...                ...              ...   \n",
       "994                           28                  1        61.435691   \n",
       "995                           24                  1        65.697122   \n",
       "996                           32                  1        58.144164   \n",
       "997                           52                  1        61.809425   \n",
       "1000                          40                  1        70.610554   \n",
       "\n",
       "             Premium_Product  \n",
       "Customer_ID                   \n",
       "1                   0.400000  \n",
       "5                   0.400000  \n",
       "6                   0.153846  \n",
       "10                  0.166667  \n",
       "11                  0.214286  \n",
       "...                      ...  \n",
       "994                 0.071429  \n",
       "995                 0.363636  \n",
       "996                 0.083333  \n",
       "997                 0.333333  \n",
       "1000                0.500000  \n",
       "\n",
       "[500 rows x 4 columns]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "campaign_cx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.884526557607702e-85\n"
     ]
    }
   ],
   "source": [
    "# ttest first\n",
    "t_stat, p_value = ttest_ind(campaign_cx['Purchase_Amount'], reg_cx['Purchase_Amount'], alternative='greater')\n",
    "print(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5277665080195835e-33\n"
     ]
    }
   ],
   "source": [
    "t_stat, p_value = ttest_ind(campaign_cx['Premium_Product'], reg_cx['Premium_Product'], alternative='greater')\n",
    "print(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "# frequency distribution\n",
    "\n",
    "num_transactions = df.groupby('Customer_ID')[['Campaign_Exposure', 'Purchase_Amount']].agg({'Campaign_Exposure':'max', 'Purchase_Amount':'count'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "exposed_fr = num_transactions[num_transactions['Campaign_Exposure']==1]\n",
    "not_exposed_fr = num_transactions[num_transactions['Campaign_Exposure']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.632537244185237e-158\n"
     ]
    }
   ],
   "source": [
    "# mann whitney\n",
    "\n",
    "u_stat, p_value = mannwhitneyu(exposed_fr['Purchase_Amount'], not_exposed_fr['Purchase_Amount'])\n",
    "print(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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