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EXERCISE 32 Let X₁,..., Xn iid Geometric(p). Show that the MLE and MM estimat ô = 1/Ã is a biased estimator of p. Show also that among all estimators of p that are bas on X₁ alone, the only unbiased estimator is p(X₁) = (1, _if X₁ = 1, |0, if X₁ = 2, 3, ……..

EXERCISE 32 Let X₁,..., Xn iid Geometric(p). Show that the MLE and MM estimat ô = 1/Ã is a biased estimator of p. Show also that among all estimators of p that are bas on X₁ alone, the only unbiased estimator is p(X₁) = (1, _if X₁ = 1, |0, if X₁ = 2, 3, ……..

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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iid EXERCISE 32 Let X₁,..., Xnd Geometric(p). Show that the MLE and MM estimator p = 1/X is a biased estimator of p. Show also that among all estimators of p that are based on X₁ alone, the only unbiased estimator is p(X₁): = 1, 0, if X₁ = 1, - 1 if X₁ if X₁ = 2, 3,....
Transcribed Image Text:iid EXERCISE 32 Let X₁,..., Xnd Geometric(p). Show that the MLE and MM estimator p = 1/X is a biased estimator of p. Show also that among all estimators of p that are based on X₁ alone, the only unbiased estimator is p(X₁): = 1, 0, if X₁ = 1, - 1 if X₁ if X₁ = 2, 3,....
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