3. Let X and Y be two independent variables taking values in 1, 2, 3, ... N. Their pmfs are given by px ( k) = py ( k) = N for k = 1, 2, 3, . . . N . (a) What is the joint pmf px,y (x, y)? Give your answer in the form of a table. Now define the random variables Z and W as Z = max {X, Y } , W = min { X, Y } (b) What values does Z take? What is the pmf pz(2)? Hint: In your table, which entries correspond to z = max{x, y} = k? (c) What values does W take? What is the pmf pw(z)