Under Uncertainty in Outcome
In case it is not possible to predict with certainty what will be the outcome of a particular decision, a probabilistic approach is necessary. In its most general form, it can be expressed as follows:
given a decision, we know the probability distribution for the possible outcomes described by the conditional probability density . We can then calculate the expected utility of decision as
- ,
where the integral is taken over the whole set (DeGroot, pp 121)
An optimal decision is then one that maximizes, just as above
Read more about this topic: Optimal Decision
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