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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 19E

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6. Let X₁, X2, ..., Xn be a random sample on the random variable that is uniformly distributed over
the interval (1,0)
(a) Find the moment estimator, 0* of and the maximum likelihood estimator 0 of 0
(b) Show that 0* is unbiased but Ô is biased
(c) Compute the bias of Ô and find the estimator ♬ that is a function of ô and unbiased.
(d) Find the variance of 0* and 7
(e) Show that both * and are consistent estimators of
(f) Find RE (7,0*) and comment on your results

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