Suppose that the random variables X and Y have joint probability density function f(x, y) = c(x^2)y if 0 x 1, 0 y 1 0 otherwise (a) Find the value of c. (b) Find marginal probability density functions fX(x) and fY (y). (c) Find E(XY ), E(X), E(Y ), and cov(X, Y ). (d) Are the random variables X and Y independent? (e) Find Pr(X Y ).