21. Let

$$f(x, y) = 24xy, \qquad 0 \le x \le 1, \ 0 \le y \le 1, \ 0 \le x + y \le 1 $$

and let it equal 0 otherwise.

(a) Show that *f(x, y)* is a joint probability density function.

(b) Find E(X).

(c) Find E[Y].