mlessentials/Chapter08/Examples/distributions.ipynb

In [0]:

import matplotlib.pyplot as plt

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# list of all xs
x = list(range(1, 11))

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print(x)

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

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# pmf
p_X_x = [1/len(x)] * len(x)

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# sums to 
print(p_X_x)

[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]

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plt.bar(x, p_X_x)
plt.xlabel('X')
plt.ylabel('P(X=x)')

Out [13]:

Text(0, 0.5, 'P(X=x)')

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import numpy as np
import scipy.stats as stats

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# range of xs
x = np.linspace(-10, 10, 100)

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# first normal distribution with mean = 0, variance = 1
p_X_1 = stats.norm.pdf(x=x, loc=0.0, scale=1.0**2)

# second normal distribution with mean = 0, variance = 2.25
p_X_2 = stats.norm.pdf(x=x, loc=0.0, scale=1.5**2)

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plt.plot(x,p_X_1, color='blue')
plt.plot(x, p_X_2, color='orange')
plt.xlabel('X')
plt.ylabel('P(X)')

Out [19]:

Text(0, 0.5, 'P(X)')