Let X1, . . . , Xn be a random sample from a Poisson distribution with mean with density function f(x) = 1 x!ex. (a) Let 0 and 1 be two given positive numbers with 1 < 0. Show that the most powerful level test for testing H0 : = 0 vs H1 : = 1 < 0 takes the form Tn k for some value of k, where Tn = n i=1 Xi. (Do not need to consider randomization test. You can cite a theorem in class to justify your asnwer.) (b) Explain how the critical value k can be determined for a level test. You may use the fact that sum of independent Poisson is Poisson. That is, if Xi P oisson(), then Xi P oisson(n)