4-54. Let X be a discrete random variable with probability mass function f (X).

If a random variable Y = a+bX, b
= 0, then the probability mass function of Y is g(y) = f y − a b

.

Verify this result when f (x) = -pX(1 − p)1−X, X = 0 or 1,0 ≤ p ≤ 1;

0 elsewhere and Y = 1 + 3X.