Question: Let X1, . . . , Xn be a random sample from a distribution with the pdf 1 e x/ , x > 0, =

Let X1, . . . , Xn be a random sample from a distribution with the pdf 1 e x/ , x > 0, = (0,). (a) Find the maximum likelihood estimator of . (b) Find the method of moments estimator of . (c) Are the estimators in a) and b) unbiased? (d) What is the variance of the estimators in a) and b)? (e) Suppose the observed sample is 2.26, 0.31, 3.75, 6.92, 9.10, 7.57, 4.79, 1.41, 2.49, 0.59. Find the maximum likelihood estimate and the method of moments estimate.

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