a) Write a computer program that simulates events that satisfy the constraints (1)-(3).

(1): A, B, C are pairwise independent

(2): P[A] = 1/4,P[B] = 1/8,P[C] = 1/16

(3): P[A B C] = 49/128 Or equivalently P[A B C] = 0

You should provide the program that you write. Specifically, let X,Y,Z be random variables. We want the output of the program to produce (X, Y, Z) such that the following four properties simultaneously hold:

• The random variables X, Y, Z are Bernoulli (i.e., binary-valued).
• P[X =1]=1/4,P[Y =1]=1/8,P[Z =1]=1/16.
• The events {X = 1}, {Y = 1}, {Z = 1} are pairwise independent.
• P[{X =1}{Y =1}{Z =1}]=0.

b) Write a paragraph to explain how you might verify that your program is working correctly

Requirements: 1 page and as needed