Question: Let X1, X2,...,Xn be i.i.d. random variables from a double exponential distribution with density f (x) = (1/2) exp(|x|). Derive a likelihood ratio test of

Let X1, X2,...,Xn be i.i.d. random variables from a double exponential distribution with density f (x) = (1/2) exp(|x|). Derive a likelihood ratio test of the hypothesis H0 : = 0 versus H1 : = 1, where 0 and 1 > 0 are specied numbers. Is the test uniformly most powerful against the alternative H1 : > 0?

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