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Possible Duplicate:
Help with conditional expectation question

I have problem with exercise, I didn't solve.

Let $X$ and $Y$ be i.i.d. random variables with $E(X)$ defined. Show that

$$E(X|X+Y)=E(Y|X+Y)= \frac{X+Y}{2}$$ (a.s.)

Thanks very much for your help.

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    I dislike the notation. $X$ and $Y$ on the right term are neither random variables nor given values (what is given is just their sum)2012-05-01
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    @leonbloy : They are random variables. Suppose the conditional expected value of the random variable $U$ given the event $V=v$, where $V$ is a random variable, is some function $g(v)$ of $v$. Then $\mathbb{E}(U\mid V=v)=g(v)$. Then one defines $\mathbb{E}(U\mid V)$ to be the random variable $g(V)$. This is perfectly standard.2012-05-01

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