Let X1, , Xn be iid Poisson() (a) Find a UMP test of H0 0 versus H1 0 (b) Consider the specific case H0 1 versus H1 1 Use the Central Limit Theorem to determine the sample size n so a UMP test satisfies P(reject H0 1) 05 and P(reject H0 2) 9

Question: Let X1,..., Xn be iid Poisson(). (a) Find a UMP test of H0: < 0 versus H1: > 0. (b) Consider the specific

Let X1,..., Xn be iid Poisson(λ).
(a) Find a UMP test of H0: λ < λ0 versus H1: λ > λ0.
(b) Consider the specific case H0 : λ < 1 versus H1 : λ > 1. Use the Central Limit Theorem to determine the sample size n so a UMP test satisfies P(reject H0|λ = 1) = .05 and P(reject H0|λ = 2) = .9.

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