In probability and statistics, the expectation or expected value, is the weighted average value of a random variable. 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. The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being. It is first assumed that X has a density f X x. Der bedingte Erwartungswert spielt eine wichtige Rolle in der Theorie der stochastischen Prozesse. Variance for a Discrete Random Variable. If x can be negative, existence of E E X: It follows directly from the discrete case definition that if X is a constant random variablei.