This article is about the term used in probability theory and statistics. For other uses, see Expected value (disambiguation). In probability theory, the expected value of a random variable, intuitively, is the long-run .. This is because an expected value calculation must not depend on the order in which the possible outcomes. Simple explanations for the most common types of expected value formula. Includes video. Hundreds of statistics articles and vidoes. Free help. The expected value (or mean) of X, where X is a discrete random variable, is a To find E[ f(X) ], where f(X) is a function of X, use the following formula: E[ f(X) ].