Anticipated value for a given investment. In statistics and probability analysis, expected value is calculated by multiplying each of the possible outcomes by the. In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents. For example Definition · Properties · Uses and applications · Expectation of matrices. Printer-friendly version. Expected Value (i.e., Mean) of a Discrete Random Variable. Law of Large Numbers: Given a large number of repeated trials, the average.