Study guide, I want to make sure I got this question right

(9) Let X and Y be iid N(0, 1) RV'S. Dene U = X+Y and V = X Y. Circle the correct answer in each of parts (a), (c), (d), (e) and show your work in part (b). (a) Do U and V have the same distribution? If so, specify the (common) distribution. 0 U and V do not share the same distribution; 0 U and V have the same distribution N (0, 2); a U and V have the same distribution which may not be normal. (1)) Show that the joint density for (U, V) is given by i serum\"). 417 (c) Are U and V independent? (1) Yes; (ii) No. ((1) The conditional mean 130' | U = V) is 1, 0, 2. (e) The conditional mean E(Y | V = 1) is 0, 1/2, 1