Suppose the random variables X and Y have joint pdf as follows: f(x, y) = 15xy^2, 0 < y < x < a. Find the marginal pdf f_1 (x) of X. b. Find the conditional pdf f_2(y | x). c. Find P(Y > 1/3 | X = x) for any 1/3 < x.< 1 d. Are X and Y independent? Justify your answer.