Difference between revisions of "Expectation (math)"
Jump to navigation
Jump to search
m |
m |
||
| Line 15: | Line 15: | ||
| − | The expectation is also the [[mean]] of | + | The expectation is also the [[mean]] of a distributed 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 00:24, January 19, 2009
The expectation of 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)
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/9ce0ff23320ca127f3d35ecea767fe6d6e5fce44)
The expectation is also the mean of a distributed variable .
The expectation with respect to some function 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)