How is Gaussian distribution calculated?

gaussian_distribution.py

# How is Gaussian distribution calculated?
# The example comes from the Numpy documentation at numpy.random.normal 
# https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html
import numpy as np
import matplotlib.pyplot as plt

# Draw samples from the distribution:
mu, sigma = 0, 0.1 # mean and standard deviation
s = np.random.normal(mu, sigma, 1000)

# Display the histogram of the samples, along with the probability density function:
# Plot the histogram
count, bins, ignored = plt.hist(s, 30, density=True)
# Plot the probability density function
plt.plot(bins, 
         1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
         linewidth=2, 
         color='r')
plt.show()