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: