04 Mean (expected value) 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

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

np.sum(df['x'] * df['P(x)'])

2.1

# Caution: linear agebra :D 
np.dot(df['x'], df['P(x)'])

2.1

# scipy.norm.mean; scipy.norm.var; scipy.norm.std but how?