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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Question 1.
Let X ...,X be a random sample from the Gamma distribution with density function
1
-ra-l,-x/B
(x > 0)
B“T(a)
where the parameters a >0, B>0 and a is known. Find
(A) The Method of Moments Estimator (MME) of B.
(B) Show that the MME in (A) is also the Maximum Likelihood Estimator (MLE) of ß.
(C) Show that the estimator found above is unbiased, consistent and its variance attains the Cramer-
Rao Lower Bound.

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