Expectation
1.
The expectation (alias
mean value
,
average
) of a
random variable X
is defined as
Example
:
2.
The expectation of a
function F=F(X)
is defined as
Example
: if
, we get
IRIT-UPS
![$E[X] = 1/2 \cdot 0 + 1/2 \cdot 1 = 1/2$](img39.gif)
,
we get 
![\begin{displaymath}E[X] = \overline{X} = \sum_{x} P_X(x) \cdot x\end{displaymath}](img38.gif)
![\begin{displaymath}E[F(X)]= \overline{F(X)} = \sum_{x} P_X(x) \cdot F(x)\end{displaymath}](img40.gif)
![\begin{displaymath}E[F(X)] = \overline{F(X)} = 1/2 \cdot \sqrt{1/2} + 1/2 \cdot \sqrt{1/2}\end{displaymath}](img42.gif){kind=small}