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Let X1, X2, ..., X, be a random sample from the exponential distribution with rate X. We will consider estimating the mean 7(A) =

 

Let X1, X2, ..., X, be a random sample from the exponential distribution with rate X. We will consider estimating the mean 7(A) = 1/A. For a simpler notation, we will define 0 = 1/A and talk about estimating 0. We already know, for any distribution, that the sample mean X is an unbiased estimator of the mean of the distribution. Define 01 = X. %3D (a) Find a second unbiased estimator of 1/A based on X(1), the minimum value in the sample. Call it 02. (b) Find the variance of both estimators of 0. Based on this, which esimator do you prefer?

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