[1} Let X and Y be independent random variables with distributions :1: 1 2 y H 1 2 3 Pram: i a i why: % i % %' Let E = XY. [i] Find E{Y]. [Answer only required.] [1] {ii} Find Var{Y}. [Answer only required] [1] {in} Write down a. table giving the probe:buiiityr distribution for Z. [Answer on}:r required.] [3] [iv] Are the random variables X and 3 independent? [Fully justify your answer] [1]