Two random variables X and Y have the joint distribution, P(0, 0) = 0.2, P(0, 2) = 0.3, P(1, 1) = 0.1, P(2, 0) = 0.3, P (2, 2) = 0.1, and P(x, y) = 0 for all other pairs (x, y).
(a) Find the probability mass function of Z = X + Y.
(b) Find the probability mass function of U = X -Y.
(c) Find the probability mass function of V = XY.