(a) A discrete random variable takes on the values 0,1,2 and 3 with probabilities 1/8, 1/4, 1/2 respectively. Determine the p.g.f of the sum of two such random variables which are independent, stating any properties of the p.g.f's that you need to use.

(b) A random variable X has density given by

f(x) = 3x^2 0 < x < 1

0 otherwise

Let Y be a new random variable defined by Y = X^2. Determine the density function of Y.