(Total 8 points) Consider a discrete pair of random variables (X,Y) with joint PMF f_{X, Y}(x, y)=\frac{1}{16}(x+y) \text { for } x=0,1 \text { and } y=0,1,2,3 = 0 otherwise.

What is the marginal PMF of Y, fy(y)? What areE(Y) and Var(Y)? ) What are E(XY) and Var(XY)? O What is Cov(X,Y)? What is the conditional PMF of X given Y, i.e., fx|y(x|y)? What is the conditional CDF of X given Y, i.e., Fx¡y(x|y)? (1 point) What are the conditional expectation and conditional variance of X given Y = 3, i.e., E(X|Y = 3) and Var(X|Y = 3)? ) Derive the CDF of X²Y.