In Example 6.8-2, take n = 30, = 15, and = 5. (a) Using the squared error loss, compute
Chapter 6, Problem 6.8-3(choose chapter or problem)
In Example 6.8-2, take n = 30, \(\alpha = 15\), and \(\beta = 5\).
(a) Using the squared error loss, compute the expected loss (risk function) associated with the Bayes estimator w(Y).
(b) The risk function associated with the usual estimator Y/n is, of course, \(\theta(1 - \theta)/30\). Find those values of \(\theta\) for which the risk function in part (a) is less than \(\theta(1 - \theta)/30\). In particular, if the prior mean \(\alpha/(\alpha+\beta) = 3/4\) is a reasonable guess, then the risk function in part (a) is the better of the two (i.e., is smaller in a neighborhood of \(\theta = 3/4\)) for what values of \(\theta\)?
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