05 Variance and standard deviation of a discrete random variable#

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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

khanacademy

Variance and standard deviation of a discrete random variable fig 1

df = DataFrame({'x': [0, 1, 2, 3, 4] ,'P(x)': [0.1, 0.15, 0.4, 0.25, 0.1]})

df
x P(x)
0 0 0.10
1 1 0.15
2 2 0.40
3 3 0.25
4 4 0.10 
mean = np.sum(df['x'] * df['P(x)'])

# caution Linear algebra 
mean = np.dot(df['x'], df['P(x)'])

var = np.sum((df['x'] - mean)**2 *  df['P(x)'])

std = np.sqrt(var)

mean

2.1

var

1.19

std

1.0908712114635715

plt.bar(df['x'], df['P(x)'])

<BarContainer object of 5 artists>
../_images/05 Variance and standard deviation of a discrete random variable_14_1.png 
sns.barplot(df['x'], df['P(x)'])

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:xlabel='x', ylabel='P(x)'>
../_images/05 Variance and standard deviation of a discrete random variable_15_2.png 
# scipy.norm.mean; scipy.norm.var; scipy.norm.std but how?