Expectation Value
المؤلف:
Papoulis, A.
المصدر:
"Expected Value; Dispersion; Moments." §5-4 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill
الجزء والصفحة:
pp. 139-152
14-2-2021
1781
Expectation Value
The expectation value of a function 
in a variable 
is denoted 
or ![E<span style=]()
{f(x)}" src="https://mathworld.wolfram.com/images/equations/ExpectationValue/Inline4.gif" style="height:15px; width:49px" />. For a single discrete variable, it is defined by
 |
(1)
|
where 
is the probability density function.
For a single continuous variable it is defined by,
 |
(2)
|
The expectation value satisfies
For multiple discrete variables
 |
(6)
|
For multiple continuous variables
 |
(7)
|
The (multiple) expectation value satisfies
where 
is the mean for the variable 
.
REFERENCES:
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.
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