Short example of a conditional normal distribution.

short_example_conditional_normal.py

import matplotlib.pyplot as plt
import numpy as np

L = np.random.multinomial(1, pvals=[1/3]*3, size=1000)
Q = L @ np.diag([1, 7, 31])
M = np.sum(Q, axis=1)

X = np.random.normal(loc=M, size=M.size)


plt.hist(X, bins=100)
plt.show()