A convenience store has two separate locations where customers can be checked out as they leave.

These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time for location 2. The joint probability function is given by

(a) Give the marginal density of both X and Y as well as the probability distribution of X given Y = 2.

(b) Give E(X) and Var(X).

(c) Give E(X | Y = 2) and Var(X | Y = 2).