Question: 1. Let (X1, X2, ..., Xn) be a random sample from an exponential distribution with probability density function f(x) given by f (20 ) =

1. Let (X1, X2, ..., Xn) be a random sample from an exponential distribution with probability density function f(x) given by f (20 ) = for x > 0; 0 , otherwise. (a Find the moment estimator A of 1. (b) Show that A is a biased estimator of A for a finite sample of size n, but becomes unbiased as n - co. Hint: You should be able to find the exact distribution of 1/1.] (c) Modify the moment estimator 1 to provide an unbiased estimator of 1, namely AMod

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