Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the followingdistribution functionf(x; 0) =xº eГ(7)В7'if x > 0elsewhereWhere, ß > 0.a) Find the maximum likelihood estimator of the parameter ß.b) Is the maximum likelihood estimator of the parameter ß unbiased or not?c) Find the variance of the maximum likelihood estimator of the parameter ß.d) What is the fisher information in the sample of size n about the parameter ß.e) What is the Cramer-Rao lower bound for the variance of unbiased estimator ofthe parameter ß?f) Is this maximum likelihood estimator an efficient estimator of ß?

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Answered: Let X₁, X2, X3, X4 be a random sample…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 1E

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