20 Free throw binomial probability distribution#

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import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats, special

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Free throw binomial probability distribution fig 1Free throw binomial probability distribution fig 2

\[ P(X) = \frac{N!}{x!(N - x)!} \pi^{x} 1-\pi^{N-x} \]
n = 6
f = 0.7

x = range(7)

y = [special.comb(n, k) * f ** k * (1-f)**(n - k) for k in x]

plt.bar(x, y)

<BarContainer object of 7 artists>
../_images/20 Free throw binomial probability distribution_9_1.png 
binom_data =stats.binom.rvs(n=6, p=0.7, size=1000)

sns.distplot(binom_data, kde=True, hist_kws={'alpha':1})
plt.xlabel('Binomial')
plt.ylabel('Frequency')

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

Text(0, 0.5, 'Frequency')
../_images/20 Free throw binomial probability distribution_11_2.png