Assume that the joint density function of random variables X and Y is given by fX;Y .x; y/ D ( 2 x y; 0 < x < 1; 0 < y < 1; 0 elsewhere. (a) Find the marginal density functions of X and Y: (b) Are the random variables X and Y independent? Justify your answer! (c) Calculate P X > 1 2 jY < 1 2 : (d) Calculate P X > 1 2 jY D 1