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The mathematical '''expectation''' of a continuously distributed variable <math>X</math> with [[probability density function]]
The mathematical '''expectation''' of a continuously distributed random variable <math>X</math> with [[probability density function]]
<math>f(x)</math> is
<math>f(x)</math> is
:<math>
:<math>
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]] <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
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>
</math>
For a discretely distributed variable <math>X</math> with [[probability mass function]]
For a discretely distributed random variable <math>X</math> with [[probability mass function]]
<math>p_{k}</math> it is
<math>p_{k}</math> it is
:<math>
:<math>