Difference between revisions of "Expectation (math)"
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| − | The mathematical '''expectation''' of a continuously distributed variable <math>X</math> with [[probability density function]] | + | The mathematical '''expectation''' of a continuously distributed random variable <math>X</math> with [[probability density function]] |
<math>f(x)</math> is | <math>f(x)</math> is | ||
:<math> | :<math> | ||
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f(x)dx. | f(x)dx. | ||
</math> | </math> | ||
| − | The expectation is also the [[mean]] | + | The expectation is also the [[mean]] <math>X</math>. |
The expectation with respect to some function <math>g(X)</math> where <math>X</math> is distributed according to <math>f(x)</math> is | The expectation with respect to some function <math>g(X)</math> where <math>X</math> is distributed according to <math>f(x)</math> is | ||
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</math> | </math> | ||
| − | For a discretely distributed variable <math>X</math> with [[probability mass function]] | + | For a discretely distributed random variable <math>X</math> with [[probability mass function]] |
<math>p_{k}</math> it is | <math>p_{k}</math> it is | ||
:<math> | :<math> | ||
Revision as of 18:02, February 22, 2009
The mathematical expectation of a continuously distributed random variable 
with probability density function
is
The expectation is also the mean .
The expectation with respect to some function 
where is distributed according to is
For a discretely distributed random variable with probability mass function
it is
