Let X have a (0) distribution, =(0, ) and = [0, 0). The loss function is L(0, a) = (0-a). Consider decision rules of the

Let X have a (0) distribution, =(0, ∞) and = [0, 0). The loss function is L(0,

a) = (0-a)². Consider decision rules of the form 8(x) cx. Assume

π(0) =e is the prior density.

(a) Calculate p(ㅠ, a), and find the Bayes action. (Note that this is the optimalBayes action for the no-data problem in which x is not observed.)

(b) Find R(0, 8).

(c) Show that & is inadmissible if c > 1.

(d) Find r(π, δ.).

(e) Find the value of c which minimizes τ(π, δ.).

(f) Find the best rule of the form de in terms of the minimax principle.