1. Suppose U; V; W are independent Poisson random variables with means ?; µ; r,, respectively. Let X D U C W; Y D V C W:
(a) Find the marginal pmfs of X and Y.
(b) Find the joint pmf of .X; Y /.
2. Suppose a fair die is rolled twice. Let X and Y be the two rolls. Find the following with as little calculation as possible:
(a) E.X C Y jY D y/.
(b) E.XY jY D y/.
(c) Var.X 2Y jY D y/.
(d) pX CY;X -Y :