Let X and Y be two jointly continuous random variables with joint PDF fx,y(x, y) = 6xy for 0 ≤ x ≤ 10,0 ≤ y ≤ x ½ and fx,y(x, y) = 0 otherwise. (a) Sketch the PDF in the x (b) Find marginal PDFs. = y plane. (c) Are X and Y independent? (d) Find the conditional PDF of X given Y = y, fxy(x│y). (e) Find E[X|Y = y], for 0 ≤ y ≤ 1. (f) Find Var(X|Y = y) for 0 ≤ y ≤ 1.