import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
np.random.seed(0)

x = np.arange(1, 1001, 1)
samples = np.random.randint(1, 7, len(x))
averages = np.cumsum(samples)/x

plt.plot((0, 1000), (3.5, 3.5), label='Theoretical mean')
plt.plot(x, averages, label='Observed averages')

plt.title('Average dice roll by number of rolls')
plt.xlabel('Number of trials')
plt.ylabel('Average')
plt.ylim((1, 6))
plt.legend()
plt.savefig('lawoflargenumbers.svg')