3. Suppose X has a Bernoulli distribution with mean q E (0, 1) and that the conditional distri- bution of Y given X has, for some pe (0, 1), probability mass function frix(y, x) = I(x = 1)p"(1 -p) + I(x =0)(1 -p)"p, yEy = {0, 1, ..., }. (a) Find the probability mass function of the random variable Z = XY. (b) Find the moment generating function of Z. (c) Find the variance of Z