Question

Directly using mathematical expression, DO NOT USE the built-in Python functions, evaluate the binomial function for n = 20, p = 3/8. Make sure you plot your results (Remember the the binomial distribution is discrete)

Answer 1

import math

import numpy as np

import matplotlib.pyplot as plt

# function to calculate binomial co-efficient

def NchooseK(n, k):

    a = math.factorial(n)

    b = math.factorial(k)

    c = math.factorial(n - k)

    ret = a/(b * c)

    return ret

def PB(x, n, p):

    ans = (NchooseK(n, x))*(p**x)*((1-p)**(n-x))

    return ans

n = 20

xx = []  # initialise array to save x values from 0 to 8

yy = []  # initialise array to save PB(x,n,p) values for p = 0.5

p = 0.375

# save PB(x,n,p) values for p = 0.375

for x in range(0, 21):

    tmp = PB(x, n, p)

    xx.append(x)

    yy.append(tmp)

    print("n = ", n, " p = ", p, " x = ", x, " PB(x, n, p) = ", tmp)

# plot the data

plt.plot(xx, yy, color="red", label='PB(x,n,p) for p = 0.375')

plt.xlabel('x')

plt.legend(loc='upper right')

plt.show()

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