A product is classified according to the number of defects X it contains and the label of the factory Y that produces it. We know that X takes values in {0, 1, 2} and Y takes values in { 1, 2}. Moreover, suppose that (X, Y) has joint PMF f(x, y) satisfying f(0, 1) = 1/8, f(0, 2) = 1/8, f(1, 1) = 1/4, f(1, 2) = 1/8, and f(2, 1) = 1/8. (a) Compute f(2,2) and the marginal PMFs fx and fy. (b) Compute the means and variances of X and Y respectively. (c) Compute Cov(X, Y) and Corr(X, Y)