Expectation (math)

The expectation of random 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> This 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>