from math import gcd
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(234)
n = 5000
xnorm = np.random.randn(n)
barxnorm = np.cumsum(xnorm) / np.arange(1, n+1)

xunif = np.random.rand(n)
barxunif = np.cumsum(xunif) / np.arange(1, n+1)

plt.figure(figsize=(10, 5))
plt.axhline(0, color='black', lw=.5)
plt.plot(np.arange(1, n+1), barxunif, label="Uniform")
plt.plot(np.arange(1, n+1), barxnorm, label="Normal")
plt.legend()

plt.savefig("law_large_numbers.png", dpi=300)