A device has been created which can supposedly classify blood as type A, , AB, or O. The device measures a quantity X, which has

A device has been created which can supposedly classify blood as type A, В, AB, or O. The device measures a quantity X, which has density f(x 0) =e_(x-( I)@( )x).

If 0 < 0 <1, the blood is of type AB; if 1<0<2, the blood is of type A; if 2<0<3, the blood is of type B; and if 0 > 3, the blood is of type O. In the population as a whole, e is distributed according to the density

π(0) = eI(a)(0).

The loss in misclassifying the blood is given in the following table.

Classified As AB A B Ο

AB 0 1 2 True A 0 2 2 Blood Type B 2 0 2

Ο 3 3 3 이

If x = 4 is observed, what is the Bayes action?