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Q29Section A (Section A)29 of 60

MP test for an exponential rate

Let X1,X2,…,XnX_1,X_2,…,X_n be a random sample from an Exp(λ)\mathrm{Exp}(\lambda) distribution, where λ∈{1,2}\lambda\in\{1,2\}. For testing H0:λ=1H_0:\lambda=1 against H1:λ=2H_1:\lambda=2, the most powerful test of size α\alpha, α∈(0,1)\alpha\in(0,1), will reject H0H_0 if and only if

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