Let X1, ..., X, be i.i.d. Gamma(o, 8) distributed and a > 0 is known. The p.d.f. is f (E) = a-1 exp(-x/B), I >0.1. Find the MLE of 8. (5 points) 2. Suppose we want to test Ho : 8 = Bo against H1 : 8 * Bo, for some known and fixed po >0. Develop a level a test for it, using the MLE as the test statistic. (15 points) 3. What is the power of your test at the point 81 # 8,? (5 points) You may use the fact that \\ X, ~ Gamma(no, B)