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. Definition of expected value & calculating by hand and in Excel. Includes video. Find an expected value for a discrete random variable. Anticipated value for a given investment. In statistics and probability analysis, expected value is calculated by multiplying each of the possible outcomes by the. Sign up using Facebook. The concept of expected value of a random variable is one of the most important concepts in probability theory. Sinai "Theory of Probability and Random Processes" Springer , Def. The expected value of a measurable function of X , g X , given that X has a probability density function f x , is given by the inner product of f and g:. The property is as follows: Der bedingte Erwartungswert ist eine Verallgemeinerung des Erwartungswertes auf den Fall, dass Gewisse Ausgänge des Zufallsexperiments bereits bekannt sind. For discrete random variables this is proved as follows: Dieser gibt an, wo sich der Hauptteil der Verteilung befindet. Let be an absolutely continuous random variable. In statistics and probability analysis, the EV is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur, and summing all of those values. The formal definition subsumes both of these and also works for distributions which are neither discrete nor continuous; the expected value of a random variable is the integral of the random variable with respect to its probability measure. Definition Let be a discrete random variable with support and probability mass function. Show that if X has a discrete distribution with density function f then. The symbol indicates summation over all the elements of the support. Provides a rigorous definition of expected value, based on the Lebesgue integral. Ist die Summe nicht endlich, dann muss die Reihe absolut konvergieren , damit der Erwartungswert existiert. This relationship can be used to translate properties of expected values into properties of probabilities, e.