(10 points) Suppose that X and Z are random variables such that P(Z = 1/4) = 1/3, P(Z = 1/2) = 1/6, P(Z = 2/3) = 1/2, and 20 P(X = x Z = z) =( 27 (1 - 2)20-1 * = 0, 1,..., 20 for z = 1/4, 1/2, 2/3. Compute E[X]