Expectation Value
The expectation value of a function 
in a variable
is denoted 
or
. For a single discrete variable, it is defined
by
 |
(1)
|
where 
is the probability
density function.
For a single continuous variable it is defined by,
 |
(2)
|
The expectation value satisfies
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
For multiple discrete variables
 |
(6)
|
For multiple continuous variables
 |
(7)
|
The (multiple) expectation value satisfies
 |  |  |
(8)
|
 |  |  |
(9)
|
 |  |  |
(10)
|
where 
is the mean
for the variable 
.
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