1. Based on a random sample of 3 observations, consider two competing estimators of the populationmean u:în =(X1 + X2 + Xa), ia = ;X1 +x2 + X34(a) Are they unbiased?(b) Which estimator is more efficient? How much more efficient?2. Let {X1, X2, ..., Xm} be an independent random sample from Poisson(A),(a) Show that both X and S² are unbiased estimator of ).(b) Calculate the Cramer-Rao Lower Bound with respective to A.(c) Which estimator should be preferred and why?

It is an important part of statistics. It is widely used. Since the question has multiple sub parts…

I. Based on a random sample of 3 observations, consider two competing estimators of the population mean µ: X + Xa + Xa), in = X1+;X2+ ;Xs 3 (a) Are they unbiased? (b) Which estimator is more efficient? How much more efficient? 2. Let {X1, X2, ..., Xn} be an independent random sample from Poisson(A), (a) Show that both X and S² are unbiased estimator of ). (b) Calculate the Cramer-Rao Lower Bound with respective to A. (c) Which estimator should be preferred and why?

I. Based on a random sample of 3 observations, consider two competing estimators of the population mean µ: X + Xa + Xa), in = X1+;X2+ ;Xs 3 (a) Are they unbiased? (b) Which estimator is more efficient? How much more efficient? 2. Let {X1, X2, ..., Xn} be an independent random sample from Poisson(A), (a) Show that both X and S² are unbiased estimator of ). (b) Calculate the Cramer-Rao Lower Bound with respective to A. (c) Which estimator should be preferred and why?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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