Suppose the random variables X and Y have joint pdf as follows: f(x, y) = 15xy², 0 < y < x < 1
a Find the marginal pdf f₁ (x) of X. b Find the conditional pdf f₂(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.