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New page: 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 a...
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>
<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>