Exercise 5.1.10

import numpy as np 
N = 1000000 
a = np.random.randint(0,2,N) 
num_0 = np.sum(a<0.5) 
num_1 = np.sum(a>=0.5) 
avg = (num_0 * 0 + num_1 * 1)/N 
print(’Average␣of␣a␣million␣random␣0-1␣samples:␣’, avg) 
X = (avg-0.5)/2/np.sqrt(N) 
print(’The␣standardized␣variable␣X␣=␣’, X)

Average of a million random 0-1 samples:  0.500099
The standardized variable X =  4.9499999999980114e-08