"python code to play with binomial distribution"

Binomial Distribution

import numpy as np
import matplotlib.pyplot as plt

def C_nk (n, k):
    # get C(n,k)
    res = 1
    for i in range(n, n-k,-1):
        res *= i
    for i in range(k,0,-1):
        res /= i
    return res

def binomProb(n, k, p):
    return C_nk(n,k) * p**k * (1-p)**(n-k)


# n = 10, P(yes) = 0.3; P(no) = 0.7
n = 10
p = 0.3
x = np.arange(n+1)
y = []
for k in x:
    y.append(binomProb(n,k,p))
    
# Draw the Binomial probability distribution
plt.bar(x,y)
plt.show()

import scipy.stats as sps

# all k>2 probability
n = 10
p = 0.3
k = np.arange(n + 1)
PX = sps.binom.pmf(k, n, p)
# 二项分布累计分布
print(sum(PX[2:]))

Bernoulli Distribution

X~B(n,p), when n=1, Binomial distribution becomes Bernoulli Distribution.
伯努利分布、两点分布、0-1分布这三种分布是同一个分布的不同名称，又都是二项分布在n=1时的特例。

概率质量函数(probability mass function，简称PMF)
累积分布函数(cumulative distribution function, 简称CDF)
离散概率分布(Discrete probability distribution)