Theexpected value refers to the long-run average outcome for certainalternatives. To obtain the expected value of perfect information forany payoff table that has probabilities associated with each state ofnature, the probabilities for each of those possible outcomes mustfirst be defined. Usually, the expected value is considered to be thesum of the weighted outcomes for a given alternative. Therefore, fromthe outcomes, if the repeated alternatives are selected over a longtime period then the average is deemed to be equal to the expectedvalue which is denoted by E(x)(Felli & Hazen, 1998).
Goingthrough the given examples, we can focus on the example 16. To obtainthe expected value of perfect information from the payoff tablegiven. First, definition of the decision alternatives is given (Felli& Hazen, 1998). In this case, the decision is for the vendors tosell sun visors or umbrellas. The second step involves the definitionof possible outcomes or rather the various states of nature that islinked with the given alternatives. If the decision is not to sellsun visors then the resulting payoff is to sell umbrellas. This meansthat an individual has two possible outcomes or alternatives, sellingsun visors or umbrellas. In the third step, probabilities areassigned to the various possible outcomes that are linked with eachand every alternative. The decision to be made by the sellers isdetermined by three factors. The factors are whether it will rain,there will be overcast skies or there will be sunshine. Theprobabilities are rain (.30), sunshine (.55) and overcast skies(.15). Lastly, the expected value is computed for each of thedecision alternative. Appropriate equation is used to compute theexpected value.
Felli,J. C., & Hazen, G. B. (1998). Sensitivity analysis and theexpected value of perfect information. MedicalDecision Making,18(1),95-109.