3) Given the following joint probability density function: f(I, y) = 10. 1(1+3/) 0

3) Given the following joint probability density function: x(1+3y2) O, elsewhere. 1/18 11. 111. w. v. Prove the function is a valid joint distribution given the intervals; (0.2 p) Are X and Y independent? Motivate. (0.2 p) Find the marginals densities; (0.2 p) Find f (yl:r); (0.2 p) Calculate P[1/4 < y < 1/2 = 1]. (0.2 p)