Consider a bivariate random vector (X , Y). The random variable X is Bernoulli with rate p E (0, 1). The conditional distribution of Y given X is: if X = 1, then Y = 0 with probability 1; if X = 0, then 1" is Poisson with mean 9 > 0 a) (7 points) Find the joint probability mass function of (X , Y). b) (7 points) Find the marginal probability mass mction of Y. c) (8 points) Find E(Y). (hint: Binge3:7: = .)