08 Example - Transforming 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

khanacademy

x_df = DataFrame({
    'X = # of makes': [0, 1, 2],
    'P(x)': [0.16, 0.48, 0.36]
})

y_df = DataFrame()

y_df['N = netgain'] = x_df['X = # of makes'] * 10 - 15
y_df['P(x)'] = x_df['P(x)']

mu_x = np.sum(x_df['X = # of makes'] * x_df['P(x)'])

mu_y = np.sum(y_df['N = netgain'] * y_df['P(x)'])

var_x = np.sum((x_df['X = # of makes'] - mu_x)**2 * x_df['P(x)'])

var_y = np.sum((y_df['N = netgain'] - mu_y)**2 * y_df['P(x)'])

std_x = np.sqrt(var_x)

std_y = np.sqrt(var_y)

print(mu_x, mu_y, var_x, var_y, std_x, std_y)

1.2 -3.0 0.48000000000000004 48.0 0.6928203230275509 6.928203230275509

mu_y == 10 * mu_x - 15

True

std_y == 10 * std_x 

True