5-14. For random variables X and Y, find the value of k that makes f (x, y) = -kxy2, 0≤ x ≤ 1 and 0 ≤ y ≤ 1;

0 elsewhere, a bivariate probability density function. Then find:

(a) The cumulative distributive function

(b) P 1

2

≤ X ≤ 3 4 , 1 4

≤ Y ≤ 1 2 

(c) F 1

2 , 13



(d) The marginal density functions of X and Y

(e) The conditional density function for Y given X