5-36. Suppose that (X,Y) is a bivariate random variable with probability density function f (x, y) = -k(x + y), 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1;

0 elsewhere.

Find:

(a) The constant k

(b) The bivariate cumulative distribution function F(t, s)

(c) Demonstrate that F 1

2 , 1 2  = P 0 ≤ X ≤ 1 2, 0 ≤ Y ≤ 1 2