Expectation (math)
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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 random 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)