The probabilities expressed in Equation (9.27) are called prior probabilities in
Bayesian jargon because they express prior knowledge about the true states of nature.
Assume that the decision maker can choose among m alternatives, A = {a1, a2,...,am},
and for a given alternative aj we assign a utility value, uji, if the future state of nature
turns out to be state si. These utility values should be determined by the decision maker
since they express value, or cost, for each alternative-state pair, that is, for each aj –si
combination. The utility values are usually arranged in a matrix of the form shown in
Table 9.1. The expected utility associated with the j th alternative would be