Consider an elevator that starts in the basement and travels upward. Let N, denote the number of people that get in the elevator at floor i. Assume the N, are independent and that N, is Poisson with mean A, Each person entering at i will, independent of everything else, get off at j with probability P. , P = 1. Let O, = number of people getting off the elevator at floor j

(a) Compute E[0,].

(b) What is the distribution of O,?

(c) What is the joint distribution of O, and O? of the coin exactly