EXERCISE 32 Let X1,..., Xn “ 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 1, if X1 = 1, P(X1) = 0, if X1 = 2, 3, .... %3D

EXERCISE 32 Let X1,..., Xn “ 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 1, if X1 = 1, P(X1) = 0, if X1 = 2, 3, .... %3D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Geometric(p). Show that the MLE and MM estimator
EXERCISE 32 Let X1,..., Xn
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
1, if X1 = 1,
0, if X1 = 2, 3, ....
P(X1)

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