Let X, Y be two random variables with the following properties. (y) = 3y^ 2 for 0 y 1 and zerlsewhere. For 0 y 1, given Y = y, X had f X|Y (x...

(y) = 3y^ 2 for 0 < y < 1 and zerlsewhere. For 0 < y < 1, given Y = y, X had f X|Y (x | y) =( 2x/ y^2) for 0 < x < y and elsewhere.

(a) Find the joint density function Y Be precise about where the values (x, y) are non-zero. Check that the joint density function integrates 1.

(b) Find the conditional density function of Y given X = x.