from random import random, seed
from matplotlib import pyplot as plt

# Run random trials random uniformly distributed from 0 to 1
N = 200
x = [i for i in range(N)]
colors = ['r', 'b', 'g', 'y']#, 'c-', 'm-', 'k-']
fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.set_ylim((0, 1))
for color_index, color in enumerate(colors):
  y = [random() for i in range(N)]
  total = [sum(y[0:i])/(i) for i in range(1, N+1)]
  ax.plot(x, total, color=color, label=str('iteration #' + str(color_index+1)))


ax.plot([0, N-1], [0.5, 0.5], 'gray', linestyle='--', label='mean of probability distribution')
handles, labels = ax.get_legend_handles_labels()
legend = ax.legend(handles=handles, labels=labels, loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_title("Number of Values vs Mean of Values")
ax.set_ylabel("Mean of values taken")
ax.set_xlabel("Number of values averaged")
fig.savefig('Mean of sample vs size of sample.svg', bbox_extra_artists=(legend,), bbox_inches='tight')
plt.show()