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Suppose $X$ and $Y$ are real-valued random variables, and $f$ and $g$ are Borel measurable real-valued functions defined on $\mathbb{R}$.

If $X$ and $Y$ are independent, then I know that $f(X)$ and $g(Y)$ are also independent.

If $X$ and $Y$ are uncorrelated, are $f(X)$ and $g(Y)$ also uncorrelated?

Thanks and regards!

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    No, and the same counterexample from the last thread works.2012-02-11
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    What have you tried? What are your thoughts on this? Have you played around with simple examples? Which ones? What have you discovered?2012-02-11
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    @cardinal: Sorry.2012-02-11
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    @Tim: There is no reason to be sorry. But, here is my point: You ask a lot of questions, many of them interesting and some of them quite insightful. It is obvious you are trying to learn. The *very* best way to learn is to play around and try things on your own. Think about the definitions, what they mean, and why they're there. Use simple examples as toy models to see what makes things work and what makes them break. Practicing this will accelerate your learning considerably.2012-02-12
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    @cardinal: Thanks for the advice! I try my best to keep my questions at high quality, but I can break down from time to time. It is just too hard sometimes. I don't have very solid foundation yet.2012-02-12

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