Question: Let X1, ...,Xn be a random sample from EXP() distribution. Null hypothesis H0 : = 0 is tested against the alternative H1 :

Let X1, ...,Xn be a random sample from EXP(λ) distribution. Null hypothesis H0 : λ = λ0 is tested against the alternative H1 : λ = λ1, where λ1 > λ0. Compare the power functions of the two tests: (i) the most powerful test and (ii) the most powerful test based on the statistic X1:n. Assume that both tests have equal probabilities of a type I error.

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