Let X~P(0), where= {1, 2}, = {a, a2, a3}, and the loss matrix is a U2 0 20 10 2 50 0 20

Let X~P(0), where= {1, 2}, = {a₁, a2, a3}, and the loss matrix is a U2 аз

0 20 10

θ

2 50 0 20

(a) Show that the Bayes rules are of the following form: decide a if x < k- (log 3)/log 2, decide

a, if k-(log 3)/(log 2) k-1. (On the boundaries of these regions, randomization is, of course, allowed.)

(b) Sketch A(S) (the lower boundary of the risk set), by finding an adequate number of Bayes risk points. (It suffices to look at kit for various integers i. This choice of k eliminates the need to worry about the boundaries of the acceptance regions.)

(c) Find the minimax rule and the least favorable prior distribution.