Question: Let X,., X be iid random variables from the shifted exponential distribution: e f(x | 0) = 0 -(x 0) x > 0, x

Let X,., X be iid random variables from the shifted exponential distribution:

Let X,., X be iid random variables from the shifted exponential distribution: e f(x | 0) = 0 -(x 0) x > 0, x < 0. (a) Previously, we found the MLE = X(1). Find the bias and MSE for this estimator. (b) Find an unbiased estimator 6(x) based on X(1). (c) Find the MSE of the estimator in (b). How does this compare with the MLE? (d) Find the MSE of the MOM estimator . How does this compare with your other two estima- tors?

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