Answer with explanation

Let Z1 N N(0, 1), 22 N N((], 1), X N U(0,1), Y N I'(1301,2601) be four independent random variables. Determine the distribution of the following random variables. Derivation is NOT required. (a) R = 5121 + 1301 (b) S = Z? + z; (c) T = 845 + 1321 ._ 262'2 (d) U = X (e) V = h1X (f) W = 51y