Anticipated value for a given investment. In statistics and probability analysis, expected value is calculated by multiplying each of the possible outcomes by the. 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. Expected value. The concept of expected value of a random variable is one of the most important concepts in probability theory. It was first devised in the 17th.