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Let X1,�,Xn be i.i.d. from N(,1) and let U1,�,Un be i.i.d. from U(0,1.pdf

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Let X1,,Xn be i.i.d. from N(,1) and let U1,,Un be i.i.d. from U(0,1). All the 2n random variables are independent. Let Yi=XiUi,i=1,,n. If the Xi and Ui are both observed, then X would be a natural estimator for . If only the products Y1,,Yn are observed, then 2Y may be a reasonable estimator for . Show that both X and Y are unbiased estimators for and determine the relative efficiency of 2Y with respect to X..

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Let X1,,Xn be i.i.d. from N(,1) and let U1,,Un be i.i.d. from U(0,1). All the 2n random variables are independent. Let Yi=XiUi,i=1,,n. If the Xi and Ui are both observed, then X would be a natural estimator for . If only the products Y1,,Yn are observed, then 2Y may be a reasonable estimator for . Show that both X and Y are unbiased estimators for and determine the relative efficiency of 2Y with respect to X.

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Let X1,�,Xn be i.i.d. from N(,1) and let U1,�,Un be i.i.d. from U(0,1.pdf

  • 1. Let X1,,Xn be i.i.d. from N(,1) and let U1,,Un be i.i.d. from U(0,1). All the 2n random variables are independent. Let Yi=XiUi,i=1,,n. If the Xi and Ui are both observed, then X would be a natural estimator for . If only the products Y1,,Yn are observed, then 2Y may be a reasonable estimator for . Show that both X and Y are unbiased estimators for and determine the relative efficiency of 2Y with respect to X.