Definition of Expectation: There are several, overlapping definitions:

• The mean of a probability distribution. If the probability distribution function is F(x) then the mean would be calculated by integrating dF(x) over the domain of the probability distribution function. The expectation operator, E[], is a linear operator per Hogg and Craig, 1995, page 55.
• In a model, the agents may have to anticipate the value of variables whose realizations may occur in the future. The values they anticipate are often called their expectations. The agents may generalize only from past realizations in a way that we can call "adaptive expectations" or they may have other information from which they hypothesize a distribution from which the realization will be drawn. From such a distribution they can calculate the mean value, and variance, and so forth. This process is one of "rational expectations.".