Let X1, X2, ... , Xn be a random sample from an exponential distribution with mean

Chapter 8, Problem 8.7-8

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Let X1, X2, ... , Xn be a random sample from an exponential distribution with mean . Show that the likelihood ratio test of H0: = 0 against H1: = 0 has a critical region of the form n i = 1 xi c1 or n i = 1 xi c2. How would you modify this test so that chi-square tables can be used easily?

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