Probability & Statistics with Python b00163d7bc794beb80e267e598a7ff9f.md

Probability & Statistics with Python.

Discrete Uniform Distribution:

Bài toán:

Code:

import math
print("input interval [a,b]")
a = int(input("input a:"))
b = int(input("input b:"))
choice = int(input("Choose: 1,P(X<k)   2,P(X >= k) "))
if choice == 1:
    k = int(input("P(X<k) replace k:"))
    prob = 1/(k-a)
    mean = (a+b)/2
    sd = math.sqrt(((b-a+1)**2-1)/12)
    print(f'P(X<{k})={round(prob, 2)}, Mean: {mean}, Standard deviation: {sd}')
else:
    k = int(input("P(X>=k) replace k:"))
    prob = 1 -(1 / (k - a))
    mean = (a + b) / 2
    sd = math.sqrt(((b - a + 1) ** 2 - 1) / 12)
    print(f'P(X>={k})={round(prob, 2)}, Mean: {mean}, Standard deviation: {sd}')

Output:

Binomial Distribution:

1:

Bài toán:

Code:

n = int(input("Enter numbers of random experiment:"))
p = float(input("Enter the probability:"))
mean = n*p
variance = n*p*(1-p)
print("the mean and variance is:",mean,"and",variance,"respectively.")

Output:

2:

Bài toán:

Code:

import math
n = int(input("Enter numbers of random experiment:"))
p = float(input("Enter the probability:"))
x = int(input(f"Number of event in {n} random experiment:"))
result = math.comb(n,x)*p**x*(1-p)**(n-x)
print("The probability is:", round(result,4))

Output:

Geometric Distribution:

Bài toán:

Code:

k = int(input("Number of the random experiment until having the event:"))
p = float(input("Probability of the event:"))
result = (1-p)**(k-1) * p
print(f"The probability that the the event appear after {k} times is: {round(result,4)}")

Output:

• Negative Binomial Distribution:

  Bài toán:

  

  Code:

  import math
  p = float(input("Probability of the event:"))
  r = int(input("Number of events:"))
  k = int(input(f"Number of the random experiment until having {r} event:"))
  result = math.comb(k-1,r-1)*p**r*(1-p)**(k-r)
  print(f"Probability that in the next {k} samples, there is {r} events is: {round(result,4)}")
  

  Output:

  

  • Poisson Distribution:

  Bài toán:

  

  Code:

  import math
  mean = float(input("Enter the mean:"))
  n = int(input("Numbers of k:"))
  ask = input("Relationship of k(or/and):")
  if ask == "or":
      result = 0
      for i in range (0,n):
          k = int(input("Enter k:"))
          result = (math.exp(-mean)*mean**k)/math.factorial(k) + result
  else:
      result = 0
      for i in range(0, n):
          k = int(input("Enter k:"))
          result = (math.exp(-mean) * mean ** k) / math.factorial(k) * result
  print(result)
  
  

  Output:

Continuous Uniform Distribution:

Bài toán:

Code:

import math
print("input interval [a,b] and x where a < b")
a = int(input("input a:"))
b = int(input("input b:"))
x = int(input("input x:"))
if a <= x <= b:
    p = 1/(b-a)
else:
    p = 0
mean = (a+b)/2
sd = math.sqrt(((b-a)**2)/12)
print(f"The probability is: {p}. The mean is: {mean}. The standard deviation is: {sd}")

Output:

Standard Normal Distribution:

Bài toán:

Code:

from statistics import NormalDist
mean = float(input("Enter your mean:"))
sd = float(input("Enter your standard deviation:"))
choice = int(input("Choose: 1, P(X < a) 2, P(X > a) 3,P(a < X < B)"))
if choice == 1:
    a = int(input("input a:"))
    result = NormalDist(mu=mean, sigma=sd).cdf(a)
elif choice == 2:
    a = int(input("input a:"))
    result = 1 - NormalDist(mu=mean, sigma=sd).cdf(a)
else:
    a = int(input("input a:"))
    b = int(input("input b:"))
    result = NormalDist(mu=mean, sigma=sd).cdf(b)- NormalDist(mu=mean, sigma=sd).cdf(a)
print("The probability is:", result)

Output:

Central Limit Theorem:

Bài toán:

Code:

import math
from statistics import NormalDist
mean = float(input("Enter your mean:"))
sd = float(input("Enter your standard deviation:"))
n = int(input("Enter your statistical sample number:"))
choice = int(input("Choose: 1, P(X < a) 2, P(X > a)"))
if choice == 1:
    a = int(input("input a:"))
    ssd = sd/math.sqrt(n) #sample standard deviation
    result = NormalDist(mu=mean, sigma=ssd).cdf(a)
elif choice == 2:
    a = int(input("input a:"))
    ssd = sd / math.sqrt(n)
    result = 1 - NormalDist(mu=mean, sigma=ssd).cdf(a)
print("The probability is:", result)

Output: