Answer all questions with explanation

Assume the number of passengers that get on a bus at the first stop is X, and it follows the Poisson distribution with mean . At the second stop, each passenger gets off the bus independently with probability p, 0 < p < 1. Let Y be the number of passengers that get off the bus. Assume no more passengers gets on the bus at the second stop.

(a) Conditioned on that n passengers get on the bus at the first stop, what is the probability that m passengers get off the bus at the second stop?

(b) Find the joint probability mass function for (X, Y ).