4-52. Let X be a continuous random variable with probability mass function f (x).

If a random variable Y = a + bX, b
= 0, then the probability density function of Y is g(y) = 1

|b| f y − a b

.

Verify this result (two separate ways) when f (x) = -3(1 − x)2, 0< ∞ < 1;

0 elsewhere and Y = 4 + 2X. What if Y = 4 − 2X? (Hint: One approach is to use this expression for g(y) directly. Another is to determine the cumulative distribution function G( f ) and then use dG dt

= g( f ).)