ABSTRACT
To analyze and understand a course of action that involves uncertainties, it is helpful to construct a probability model that lists the probabilities of all possible outcomes in a particular situation or experiment. Often we are interested in knowing the gains or losses associated with each outcome, and the expected value that can be anticipated. The expected value indicates the long-run gain or loss that occurs after many independent repetitions. This numerical value can provide valuable information in making rational decisions in the face of uncertainties. In particular, its value can guide the determination of optimal mixed strategies in two-person zero-sum games. Moreover, the appropriate use of expected values can explain several paradoxical situations.
