converges, the sum
is well-defined. Its value is called the expected value, expectation or mean of . It is usually denoted by .
Taking this idea further, we can easily generalize to a continuous random variable with probability density by setting
if this integral exists.
Note that the expectation does not always exist (if the corresponding sum or integral does not converge, the expectation does not exist. One example of this situation is the Cauchy random variable).
where the integral is understood as the Lebesgue-integral with respect to the measure .
|Date of creation||2013-03-22 11:53:42|
|Last modified on||2013-03-22 11:53:42|
|Last modified by||mathwizard (128)|