1. (MGF of Bivariate Poisson). 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: Find the joint mgf of X; Y and hence E.XY /.
2. (Joint MGF). In repeated throws of a fair die, let X be the throw in which the first six is obtained and Y the throw in which the second six is obtained. Find the joint mgf of X; Y and hence the covariance between X and Y.