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3. Let X1 and X2 be i.i.d. exponential random variables with scale parameter 0, i.e., the pdf is f(x; 0) = -e- x > 0.

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3. Let X1 and X2 be i.i.d. exponential random variables with scale parameter 0, i.e., the pdf is f(x; 0) = -e- x > 0. (a) Find a sufficient statistic for 0.(b) Show that both of the following estimators of 0 are unbiased: . X, the sample mean of X1 and X2; . 2X(1), where X(1) is the minimum of X1 and X2. (c) Calculate Eff(X, 2X(1)), the efficiency of X compared to 2X(1). Which estimator is more desirable

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