#%%

import numpy as np
import matplotlib.pyplot as plt

p, trials = 0.70, 30  # probability of success & number of trials
heads, laplace, mean = [], [], []

for n in range(1, trials+1):

    h = (np.random.rand(n) < p).sum()  # no. of success in n trials

    lp = (h+1)/(n+2)
    laplace.append(lp)  # record laplace's rule

    m = h/n  # mean number of heads in the n trials
    mean.append(m)  # record the mean no. of success in n trials

# plotting the results using this guide:
# https://matplotlib.org/stable/gallery/lines_bars_and_markers/barchart.html

width, location = 0.35, np.arange(len(mean))

plt.rcParams.update({'font.size': 6})
plt.figure(figsize=(32,18))

fig, ax = plt.subplots()
rect1 = ax.bar(location - width/2, laplace, width, label='laplace')
rect2 = ax.bar(location + width/2, mean, width, label='mean')

# configurate how the graph looks
ax.set_xticks(location)
ax.set_xticklabels(location+1)
ax.set_xlabel('number of trials')
ax.set_ylabel('estimate of p')
ax.set_title('true p = 0.70')
ax.legend()

# uncomment to save the plot
# plt.savefig('fig.png', facecolor="w", bbox_inches='tight', dpi=300)

plt.show()


# %%