## ML: Advanced Probabilistic Methods
## Exercise 1, Problem 1: Coins

import matplotlib.pyplot as plt
import numpy as np

# define some variables:
theta_2 = 0.5
pi_1 = 0.5

# compute posterior probability of c_1
theta_1 = # choose a reasonable range
post_c1 = # posterior

# plot the result
plt.plot(theta_1, post_c1)
plt.title('$p(C = c_1 \\mid X = t)$ as a function of $\\theta_1$')
plt.xlabel('$\\theta_1$')
plt.show()