Difference between revisions of "Expectation (math)"
Jump to navigation
Jump to search
m |
m |
||
| Line 7: | Line 7: | ||
f(x)dx. | f(x)dx. | ||
</math> | </math> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
The expectation is also the [[mean]] of a distributed variable <math>X</math>. | The expectation is also the [[mean]] of a distributed variable <math>X</math>. | ||
| Line 23: | Line 15: | ||
g(x) | g(x) | ||
f(x)dx. | 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> | </math> | ||
[[category:Probability and Statistics]] | [[category:Probability and Statistics]] | ||
Revision as of 00:59, February 22, 2009
The mathematical expectation of a continuously distributed variable with probability density function is
![{\displaystyle {\mbox{E}}[X]=\int \limits _{-\infty }^{\infty }xf(x)dx.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9cc4a1723078d7a453b6541d844edf798c377f05)
The expectation is also the mean of a distributed variable .
The expectation with respect to some function where is distributed according to is
![{\displaystyle {\mbox{E}}[g(X)]=\int \limits _{-\infty }^{\infty }g(x)f(x)dx.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46ed321df16947ba8913e344b3bedd17e451005f)
For a discretely distributed variable with probability mass function it is
![{\displaystyle {\mbox{E}}[X]=\sum _{k}p_{k}x_{k}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3680c282419a8c960e43e5541dd016022f625617)