Let us have independent random variables X1, X2 Furthermore, let denote U=X+X2 and V = 1. Derive the joint PDF of (U, V) 2. Find the marginal distributions of U and V. ~ Gamma(a, ), i = 1,2 with a > 0, > 0. 3. Find the conditional distributions fu(ulu) and fv (v|u) 4. Are U and V independent? State the reason for your conclusion.