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Q30Section A (Section A)30 of 60

Power of Poisson likelihood ratio test

Let X1,X2,X3,X4X_1, X_2, X_3, X_4 be a random sample from a Poisson distribution with unknown mean λ>0\lambda > 0. For testing the hypothesis H0:λ=1H_0: \lambda=1 against H1:λ=1.5H_1: \lambda=1.5, let β\beta denote the power of the test that rejects H0H_0 if and only if ∑i=14Xi≥5\sum_{i=1}^4 X_i \ge 5. Then which one of the following statements is true?

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