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In an experiment, suppose X1; : : : ; Xnjθ is i.i.d with density f(xjθ) =...

In an experiment, suppose X1; : : : ; Xnjθ is i.i.d with density f(xjθ) = θe^(-xθ); 0 ≤ x > 1; θ > 0,
and the prior distribution of θ is Exponential distribution with density π(θ) = (1/β) * e^(-θ/β), where β is a
known positive constant.
(a) (15pts) Find the posterior distribution of θ.
(b) (5pts) Find the Bayes estimator of θ (the Bayes rule estimator with respect to the squared error
loss).
1
(c) (10pts) Find the Bayes rule estimator of θ with respect to the absolute error loss.

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