Please make sure that the handwriting is readable. Show all necessary steps and reasons. Define all symbols or terms carefully.

2. Let X1 X2 ..*n be a random sample from the Poisson distribution with parameter 8. Consider the hypothesis: Ho:0 = 0, vs Ha:0 # 00 a. Construct a size-a test using the generalized likelihood ratio principle. (Hint: Steps for answering: (a) Construct 1 first. Simplify the ratio. Note that X is the MLE for 8. Also sup L(8 (x) is just equal to L(8(x). (b) Set up the test $ (x) (c) Set up a rule in finding k. No need to find k itself