Let X1, X2, ..., X, be a random sample from the exponential distribution with rate X....

 

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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) = 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? 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?