Let X Y Be Two Random Variables With The Following Properties Y 3y 2 For 0 Y 1 A

(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.