Question: 2) Let X1, X 2, , Xn be random variables each has an exponential distribution with parameter %.The probability density function (p .d f. )

2) Let X1, X 2, , Xn be random variables each has an exponential distribution with parameter %.The probability density function (p .d f. ) is given by: 1 '_x f(x)=ie/1 , x>0, /1>0 Consider the estimator 9 = n Xm = n * min(X1,X2, ...,Xn). a) Show that 9' = n X (1) is unbiased estimator of A b) Find the MSE() c) Find the mle 2: of A. Is it a Sufcient statistic? d) Which estimator will you choose between the two estimators {9 and it and why? Show your work

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