Question 5 16 pts Suppose that Y1 has a gamma distribution with parameters (11 and B, that Y2 is gamma distributed with parameters 02 and I3, and that Y1 and Y2 are independent. Let U1 = Y1! Y2 and U2 =Y2. [4 points]:A. Derive the joint density function for U1 and U2. [4 points]:B. Obtain the marginal distribution of U1 [4 points]:c. Obtain the marginal distribution of U2 [4 points]:D. Are U1 and U2 are independent or not? Why or why not? Part II: (4 Points). Be sure to show a" work for full credit. Given the following moment generating function: m(t) = [O.2exp(t)+ 0.8)]6 Obtain the mean and variance