Expectation Value

The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by


where P(x) is the probability density function.

For a single continuous variable it is defined by,


The expectation value satisfies


For multiple discrete variables


For multiple continuous variables


The (multiple) expectation value satisfies


where mu_i is the mean for the variable i.

See also

Central Moment, Estimator, Maximum Likelihood, Mean, Moment, Raw Moment, Wald's Equation

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Papoulis, A. "Expected Value; Dispersion; Moments." §5-4 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 139-152, 1984.

Referenced on Wolfram|Alpha

Expectation Value

Cite this as:

Weisstein, Eric W. "Expectation Value." From MathWorld--A Wolfram Web Resource.

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