|
Sponsored Links
In probability theory and statistics, the expected value (or expectation value, or mathematical expectation, or mean) of a random variable is the integral of the random variable with respect to its probability measure. For discrete random variables this is equivalent to the probability-weighted sum of the possible values, and for continuous random variables with a density function it is the probability density -weighted integral of the possible values. 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. The value may not be expected in the general 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 all distributions, such as the Cauchy distribution. It is possible to construct an expected value equal to the probability of an event by taking the expectation of an indicator function that is one if the event has occurred and zero otherwise. This relationship can be used to translate properties of expected values into properties of probabilities, e.g. using the law of large numbers to justify estimating probabilities by frequencies. The expected value from the roll of an ordinary six-sided die is
|
Expected Value Subcategories
Expected Value Articles
|
| 
