Let X and Y be iid N(0; 1) RV's. Define U = XY and V = X/Y.

Please explain the steps to get the answer

Let X and Y be iid N(0, 1) RV's. Define U = XY and V = X/Y. . Note: UV = X2 and U/V = Y2 hence we have the restriction D = {u > 0, v > O} U fu (x, y) has its absolute value 1 2 . . Step 2: The joint density fu, v) ( u, v ) = u 2 J ( X, X) ( U, u / V ) = 2 TV/2 12 (1 +v-2)/2, (u, v) ER . Step 3: The marginal density fv ( v) = / f ( U, V) (u, v) du = ... = R TT ( V 2 + 1 ) VER. . Note: U serves as an auxiliary variable which can be defined arbitrarily as long as it is easy to integrate it out