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From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: question about the expected value of this distribution
Date: Thu, 8 Mar 2012 14:33:18 +0000 (UTC)
Organization: Xoran Technologies
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Xref: news.mathworks.com comp.soft-sys.matlab:760357

>
> 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).
```