The number of people who enter elevator on the ground floor is a Poisson random variable with mean ten. There are five floors above the ground floor, and each person is equally likely to exit the elevator at any of the five floors, independently of where the others exit.
Using the fact that X is Poisson with parameter lambda, and it has the corresponding moment generating function: show that the number of people who exit the elevator on the kth floor has a Poisson distrubution with mean 2.