3 2) Consider the region S of the plane given by S = [-1, 1] x [-2, 2] U [1, 2] x [-1, 1] i.e. S is the union of the rectangle with vertices (-1, -2), (-1, 2), (1, 2), (1, -2) and the rec- tangle with vertices (1, -1), (1, 1), (2, 1), (2, -1). Let X, Y be two r.v. with a joint uniform PDF fxY. (a) Find the conditional PDF's frix(ylx) and fxy(xly) for various relevant values of r and y. (b) Find E(X|Y), E(X) and var(X|Y). Use these to calculate var(X). (c) Find E(Y X), E(Y) and var(Y X). Use these to calculate var(Y)