Difference between revisions of "Expectation (math)"

Latest revision as of 12:16, July 13, 2016

The mathematical expectation of a continuously distributed 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> The expectation is also known as the mean of <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 random 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>

@@ Line 1: / Line 1: @@
-The '''expectation''' of 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>
@@ Line 7: / Line 7: @@
 f(x)dx.
 </math>
+The expectation is also known as the [[mean]] of <math>X</math>.
-For a discretely distributed variable <math>X</math> with [[probability mass function]]
+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>p_{k}</math> it is
-:<math>
-\mbox{E}[X] =  \sum_{k} p_{k}x_{k}
-</math>
-The expectation 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)]
@@ Line 25: / Line 17: @@
 </math>
-[[category:Probability and Statistics]]
+For a discretely distributed random 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>
+[[Category:Probability and Statistics]]