Suppose there are 4 possible actions, ai, i = 1,2,3,4, and three possible states of nature, Oi, i = 1.2,3, in a decision problem, and we have the loss matrix:

Loss a 02 03 5 04 e 5 2 6 1 02 4 3 1 2 0, 0 8 2 9. Suppose the prior probabilities for are as shown in the following table: Prior Probabilities 8 Bz 83 Prior Probability 0.3 0.2 0.5 First note that action a dominates action a since the losses are smaller, regardless of the state of nature. So a need not be considered further in any decision problem. Assuming no data are available, find a suitable Bayes' decision rule.