4.II.19H
It is required to estimate the unknown parameter after observing , a single random variable with probability density function ; the parameter has the prior distribution with density and the loss function is . Show that the optimal Bayesian point estimate minimizes the posterior expected loss.
Suppose now that and , where is known. Determine the posterior distribution of given .
Determine the optimal Bayesian point estimate of in the cases when
(i) , and
(ii) .
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