USE AND ENJOY THE BINOMIAL DISTRIBUTION MODEL

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

import scipy.stats as stats

from scipy.stats import binom



%matplotlib inline



# Standard notation

# P = binomial probability

# x = number of times for a specific outcome within n trials

# n = number of trials

# p = probability of success on a single trial

# q = probability of failure on a single trial

# k = an array of n, the number of trials

# p_of_k = probabilty of successes for each trial

# am = at most = Define at most successes

# Probability mass function = .pmf()

# Probability density function = .pdf()

# The probability mass function of the binomial distribution is

# f(x)=P[X=x]=(nx)px(1−p)n−x



n = (10)

p = (0.8)

k = np.arange(0,11)

am = (6)



p_of_k = binom.pmf(n,n,p)

p_of_k



x = binom.pmf(k,n,p)

x



barl = plt.bar(k, x, color='hotpink')

plt.title(('When p =  ' + str(p) + ' and at most ' + str(am) + ' successes'), fontsize=13, color='r')

plt.legend((p, ''), fontsize=10)

plt.xlabel('Number of Successes', fontsize=10, color='r')

plt.ylabel('Probability of Successes', fontsize=10, color='royalblue')

for i in range(0, am):

    barl[i].set_color('r')