Introduction to the Normal distribution

Statistical Thinking in Python (Part 1)

Justin Bois

Teaching Professor at the California Institute of Technology

Normal distribution

Describes a continuous variable whose PDF has a single symmetric peak.

Normal distribution

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Normal distribution

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Normal distribution

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Normal distribution

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Normal distribution

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Comparing data to a Normal PDF

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Checking Normality of Michelson data

import numpy as np
rng = np.random.default_rng()

mean = np.mean(michelson_speed_of_light)
std = np.std(michelson_speed_of_light)

samples = rng.normal(mean, std, size=10000)
x, y = ecdf(michelson_speed_of_light)
x_theor, y_theor = ecdf(samples)

Checking Normality of Michelson data

import matplotlib.pyplot as plt
import seaborn as sns
sns.set()
_ = plt.plot(x_theor, y_theor)
_ = plt.plot(x, y, marker='.', linestyle='none')
_ = plt.xlabel('speed of light (km/s)')
_ = plt.ylabel('CDF')
plt.show()

Checking Normality of Michelson data

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Let's practice!

Statistical Thinking in Python (Part 1)