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Estimator of the Form of Linear Statistic

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Given "X[1, ]X[2,]..... X[n]" form a random sample from an exponential λ distribution, find the estimator of the form "T[a]= a/(sum( X[i])" with the smallest mean square error as an estimator of λ.

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The solution provides a step-by-step explanation on how we find the estimator which minimizes the mean square error. Please see attachment for further details.

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