Let X have a distribution, and The loss function is Consider decision rules of the form Assume is the prior density. (a) Calculate and find the Bayes action. (Note that this is the optimal...

Let X have a

distribution,

and

The loss function is

Consider decision rules of the form

Assume

is the prior density.

(a) Calculate

and find the Bayes action. (Note that this is the optimal Bayes action for the no-data problem in which x is not observed.)

(b) Find

(c) Show that

is inadmissible if c> 1.

(d) Find

(e) Find the value of c which minimizes

(f) Is there a best rule of the form

in terms of the minimax principle?