def prob_5a():
pi, P, T = problem_data.hw2_p5_data()
probs = np.zeros(T)
for time in range(T):
probs[time] = pi[0]
pi = np.dot(pi, P)
utils_io.label('2.5a')
print 'p_T for T={0:d} equals: {1:f}'.format(T-1, np.mean(probs))
def prob_5b():
num_samples = np.array([10, 100, 1000, 10000])
avg_ones = np.zeros(len(num_samples))
pi, P, T = problem_data.hw2_p5_data()
for idx, num in enumerate(num_samples):
ones = []
for sample in range(num):
number_of_ones = 0
next_dist = pi
for time in range(T):
next_idx = get_random_idx(next_dist)
if next_idx == 0:
number_of_ones += 1
next_dist = P[next_idx]
ones.append(number_of_ones)
avg_ones[idx] = np.mean(ones) / T
utils_io.label('2.5b')
print 'num in sample: ', num_samples
print 'p_T estimate for T={0:d} equals: {1:s}'.format(T-1, avg_ones)
