2. Let (X, Y) be a vector with joint density function x+y 3 fx,y (x, y) = (2) 1(0,1,2,3,...) (y) (yu+1,y+2,...} (x) a) Determine E[X], E[Y], Var[X], and Var[Y]. b) Determine E(X,Y) and Cov(X, Y). c) Determine Var(X, Y) and p(X, Y). d) Determine the moment-generating function of X and Y.

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