Difference between revisions of "Expectation (math)"
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m (Expectation moved to Expectation (math): esoteric) |
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| − | The '''expectation''' of | + | The '''expectation''' of continuously distributed 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> | ||
| − | + | ||
| + | For a discretely distributed variable <math>X</math> with [[probability mass function]] | ||
| + | <math>p_{k}</math> it is | ||
| + | :<math> | ||
| + | \mbox{E}[X] = \sum_{k} p_{k}x_{k} | ||
| + | </math> | ||
| + | |||
| + | |||
| + | The expectation is also the [[mean]] of random variable <math>X</math>. | ||
The expectation with respect to some function <math>g(X)</math> is | The expectation with respect to some function <math>g(X)</math> is | ||
Revision as of 23:53, January 18, 2009
The expectation of continuously distributed variable <math>X</math> with probability density function <math>f(x)</math> is
- <math>
\mbox{E}[X] =\int\limits_{-\infty}^\infty x f(x)dx. </math>
For a discretely distributed variable <math>X</math> with probability mass function <math>p_{k}</math> it is
- <math>
\mbox{E}[X] = \sum_{k} p_{k}x_{k} </math>
The expectation is also the mean of random variable <math>X</math>.
The expectation with respect to some function <math>g(X)</math> is
- <math>
\mbox{E}[g(X)] =\int\limits_{-\infty}^\infty g(x) f(x)dx. </math>