import numpy as np
import matplotlib.pyplot as plt

# Define the Gaussian distribution
mu, sigma = 0, 5  # High variance
gaussian = np.random.normal(mu, sigma, 1000000)  # Generate a lot of samples

# Rejection sampling
gaussian = gaussian[(gaussian > -1) & (gaussian < 1)]

# Generate uniform distribution
uniform = np.random.uniform(-1, 1, len(gaussian))  # Same number of samples as the Gaussian

# Plot the distributions
plt.figure(figsize=(12,6))

plt.subplot(1, 2, 1)
plt.hist(gaussian, bins=30, density=True, alpha=0.6, color='g')
plt.title('Gaussian Rejection Sampling')

plt.subplot(1, 2, 2)
plt.hist(uniform, bins=30, density=True, alpha=0.6, color='b')
plt.title('Uniform Distribution')

plt.show()