(15 points) Let X, X2, ..., X, be an i.i.d. sample from a density given by...

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(15 points) Let X₁, X2, ..., X, be an i.i.d. sample from a density given by fe(r) = e for x € R. a) Find Method of Moments Estimator for 0. (4p) b) Find Maximum Likelihood Estimator for 9. (4p) c) Calculate the efficiency of the estimator in b). Exact, not approximate. (5p) d) Which of the estimators is sufficient statistic? (justify your answer) (2p) (15 points) Let X₁, X2, ..., X, be an i.i.d. sample from a density given by fe(r) = e for x € R. a) Find Method of Moments Estimator for 0. (4p) b) Find Maximum Likelihood Estimator for 9. (4p) c) Calculate the efficiency of the estimator in b). Exact, not approximate. (5p) d) Which of the estimators is sufficient statistic? (justify your answer) (2p)