Exercise 1 (3 + 3 points). In the lectures, we learned that if X and Y are independent continuous random variables with pdfs J"); and fy, then ism/(z) : f... men/(z w) dw. (1) In the lectures I also said (incorrectly) at s0me point that it is not possible to derive this expression from our \"Jacobian\" method. In this exercise, we will show how to derive the expression above using the J acobian method. 1. Dene V : X and U : Y + X. Using the Jacobian method, derive the joint distribution of (U, V). 2. Note that the distribution of interest is U : X +Y. So, using the joint pdf in part (1), nd the marginal distribution of U and compare it to the expression in equation (1). They should match. Thus, this approach gives us a way to derive the distribution of X + Y using the Jacobian method