Let X1, ,Xn be a random sample from the POI() distribution Find the (approximate) UMPU test for the hypothesis H0 0 against the two sided alternative H1 0, where 0 is assumed to be large Hint Use the fact that if X has Poisson distribution with mean , then (X ) converges (as ) in the distribution to a standard normal random variable

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Question: Let X1, ...,Xn be a random sample from the POI() distribution. Find the (approximate) UMPU test for the hypothesis H0 : = 0 against

Let X1, ...,Xn be a random sample from the POI(λ) distribution. Find the (approximate) UMPU test for the hypothesis H0 : λ = λ0 against the two-sided alternative H1 : λ

= λ0, where λ0 is assumed to be large. [Hint: Use the fact that if X has Poisson distribution with mean λ, then (X − λ)/

√

λ converges (as λ → ∞) in the distribution to a standard normal random variable.]

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