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 <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> The expectation is also the mean of a distributed variable <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
- <math>
\mbox{E}[g(X)] =\int\limits_{-\infty}^\infty g(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>