Two random variables X and Y have the following joint probability density function: fxY (x, y) = Jc(xty) 0

Two random variables X and Y have the following joint probability density function: c(a; + y) 0 < y f x S 1 fxy(X, Y) 0 elsewhere- (i) (5 points) Find c. (ii) (5 points) Find the pdf of Y, fy(y). (iii) (5 points) Find E(XIY). (iv) (5 points) Are X and Y independent? Justify your answer. (v) (5 points) Let Z (2y + 1)2. Find the pdf of Z, fz(z). Solution (You can use the back of the page too)