Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2 and scale parameter 0, where > 0 is unknown. a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of your unbiased estimator. b. Find two unbiased estimators of 7(0) = 0².

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter
a = 2 and scale parameter 0, where > 0 is unknown.
a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of
your unbiased estimator.
b. Find two unbiased estimators of 7(0) = 0².
Transcribed Image Text:Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2 and scale parameter 0, where > 0 is unknown. a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of your unbiased estimator. b. Find two unbiased estimators of 7(0) = 0².
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