Let Y,,Y,.,Y, be a random sample of size n from the gamma, distribution with probability density function f; (y;0) = -yle®, y>0. (r-1):0" (i) Show that ô = -Y is an unbiased estimator of 0. r

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
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Let Y,,Y,.,Y, be a random sample of size n from the gamma, G
distribution
with probability density function
f; (y;0) =-
1
-y"-'e*® , y >0.
(r-1):0"
(i)
Show that ô = -7
is an unbiased estimator of 0.
(ii)
Obtain the Cramer-Rao lower bound for the variance of an unbiased
estimator of 0.
Transcribed Image Text:Let Y,,Y,.,Y, be a random sample of size n from the gamma, G distribution with probability density function f; (y;0) =- 1 -y"-'e*® , y >0. (r-1):0" (i) Show that ô = -7 is an unbiased estimator of 0. (ii) Obtain the Cramer-Rao lower bound for the variance of an unbiased estimator of 0.
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