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LetX1,...,Xnbe a random sample from a continuous distribution with the probability densityfunction (pdf) with an unknown...

LetX1,...,Xnbe a random sample from a continuous distribution with the probability densityfunction (pdf) with an unknown parameterθ:fX(x;θ) ={e−(x−θ), x > θ,0,otherwise.Assume that the prior distribution ofθhas the following density:fΘ(θ) ={2e−2(θ−1), θ >1,0,otherwise.(a) For the observed data 2.1,1.5,1.8,2.3,1.6 (n= 5), find the posterior density ofθ.

For the data in (a), find the Bayes estimates ofθunder the squared and absolute loss.

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