# Question

Let Y be the largest order statistic of a random sample of size n from a distribution with pdf f(x | θ) = 1/θ, 0 < x < θ. Say θ has the prior pdf

where α > 0, β > 0.

(a) If w(Y) is the Bayes estimator of θ and [θ − w(Y)]2 is the loss function, find w(Y).

(b) If n = 4, α = 1, and β = 2, find the Bayesian estimator w(Y) if the loss function is |θ − w(Y)

where α > 0, β > 0.

(a) If w(Y) is the Bayes estimator of θ and [θ − w(Y)]2 is the loss function, find w(Y).

(b) If n = 4, α = 1, and β = 2, find the Bayesian estimator w(Y) if the loss function is |θ − w(Y)

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