Consider a random sample X1, X2, ..., Xn from a distribution with probability function: f(x, 0) = 0(10) I {0,1,2....}(x) a. Find the uniformly most powerful (UMP) test for testing the hypothesis Ho 0 0 against H : 0 > Oo. VS b. Find the likelihood ratio (LR) test for testing the hypothesis Ho00o vs H : 000 and compare (to see whether they are equivalent or not) with the union intersection test (UIT) constructed from the two one-sided UMP tests. c. By inverting the UIT or the LR test, find a 95% exact CI for 0 and 11. d. Find an exact and asymptotic (large sample) 95% CIs for 1-0.