Expected Value

In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or the first moment) of a random variable is the weighted average of all possible values that this random variable can take on. The weights used in computing this average correspond to the probabilities in case of a discrete random variable, or densities in case of a continuous random variable. From a rigorous theoretical standpoint, the expected value is the integral of the random variable with respect to its probability measure.

The expected value may be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity. More informally, it can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll). The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), just like the sample mean.

The expected value does not exist for some distributions with large "tails", such as the Cauchy distribution.

Read more about Expected Value:  History, Uses and Applications, Expectation of Matrices

Famous quotes containing the word expected:

    What is a country without rabbits and partridges? They are among the most simple and indigenous animal products; ancient and venerable families known to antiquity as to modern times; of the very hue and substance of Nature, nearest allied to leaves and to the ground,—and to one another; it is either winged or it is legged. It is hardly as if you had seen a wild creature when a rabbit or a partridge bursts away, only a natural one, as much to be expected as rustling leaves.
    Henry David Thoreau (1817–1862)