A convenience store has two separate locations in the store where customers can be: checked out as they leave. These locations both have: two cash registers and have two employees that check out customers. Let X be the number of cash registers being used at a particular time for location L and Y the number being used at the same: time period 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 A" given V = 2.(b) Give E(X) and Var(X).(c) Give E(XY = 2) and Var(X|Y =2).

1 0.12 0.04 0.04 0.19 0.05 0.12 0.30 0.08 0.06 21