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Subject: Re: question about the expected value of this distribution
Date: Thu, 8 Mar 2012 14:33:18 +0000 (UTC)
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"anja.ende@googlemail.com" <anja.ende@googlemail.com> wrote in message <63344cb9-ead9-4235-bb13-de80516e0c66@q11g2000vbu.googlegroups.com>...
>
> I have a joint entropy like expression as follows:
> 
> F(B|A) = integral[-inf +inf] P(B>b|A) log P(B>b|A)
================

Is the integration w.r.t. b? If not then what? And if so, shouldn't F simply be a function of the single random variable A?

F(A) = integral[-inf +inf] P(B>b|A) log P(B>b|A)

I'll assume so below.


> Now, what would be the expected value of this expression i.e. E(F(B|
> A)). Would it be simply scaling over the sum of each of the rows and
> columns? I am somehow getting very confused with this.
> 
================

E(F(A))= sum F(A) P(A)

The probabilities P(A) can just be obtained as the marginal of your 
joint distribution P(A,B).