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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: Why is the expected value not zero if theta = 0?''
by stevecheng on 2005-10-07 18:20:17 |
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| It is a definition. In probability theory,
E[X] is simply an abbreviation for the Lebesgue integral
\int_\real x dP_X(x)
where dP_X is the probability distribution for the random variable X.
And such an integral is not considered to exist if
\int_\real |x| dP_X(x) = \infty.
Why? Mainly because "conditionally convergent" integrals
behave badly in some ways; this was discussed before in a previous
thread.
// Steve
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