5-13. Given the bivariate probability density function f (x, y) = -3x(1 − xy), 0 < x < 1 and 0 < y < 1;

0 elsewhere, find:

(a) P X ≤ 1 2 , Y ≤ 1 2 

(b) the marginal densities of X and Y

(c) P 1

4 < X < 13

, 13

< Y < 1 2 

(d) The conditional density function of X given Y

(e) The conditional density function of Y given X Are the random variables X and Y independent?