Let X be a Bernoulli random variable with P(X = 1) = p and P(X = 0) =1 -p. For each i E Sx, given that X = i, Y has a Poisson distribution with parameter (i + 1). (a) (7 points) Find the PMF of Y. (b) (5 points) Find the conditional probability P(X = 0|Y = 0). (c) (5 points) Let Z = X + Y. Find E[Z|X = 0] and E[Z |X = 1]. (d) (3 points) Use your answers in part (c) to find E[Z]