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Problem 1: Let X₁, X2, ..., X be a random sample from a Poisson distribution. Find the likelihood ratio for testing Ho: λ = λ versus H₁: λ=₁, where λ₁ >

. Use the fact that the sum of independent Poisson random variables follows a Poisson distribution to explain how to determine a rejection region for a test at level a.

Fig: 1