Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Computer Science Posted 26 Aug 2017 My Price 9.00

distributed population

Let Y1, Y2, . . . , Yn denote a random sample from an exponentially distributed population with density f (y | θ) = θe−θ y , 0y. (Note: the mean of this population is μ = 1/θ.) Use the conjugate gamma (α, β) prior for θ to do the following.

a Show that the joint density of Y1, Y2, . . . , Yn, θ is

               

b Show that the marginal density of Y1, Y2, . . . , Yn is

               

e Show that the Bayes estimator in part (d) can be written as a weighted average of  and the prior mean for 1/θ

f Show that the Bayes estimator in part (d) is a biased but consistent estimator for μ = 1/θ.

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Maurice Tutor
(5)
Status NEW Posted 26 Aug 2017 09:08 PM My Price 9.00

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