Showing that $\mathsf{Cov}(f(X), g(Y)) \geq 0$ for non-decreasing $f$ and $g$ taking values on $\mathbb{R}$.

Asked Oct 04 '17 at 22:34

Active Oct 04 '17 at 23:02

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We have two non-decreasing functions $f$ and $g$ and a random variable $X$. We want to show that $\mathsf {Cov}(f(X),g(X))\geqslant 0$.

Intuitively, it makes sense, but how do I formalize this?

edited Oct 04 '17 at 23:02

Graham Kemp

asked Oct 04 '17 at 22:34

anktsdmcknsy

What are "non-decreasing $X$ and $Y$"? – Oct 04 '17 at 22:48
@d.k.o. I have tried to simplify the problem from what it originally was. We have two non-decreasing functions $f$ and $g$ and a random variable $X$. We want to show that Cov$(f(X), g(X)) \geq 0$. – anktsdmcknsy Oct 04 '17 at 22:52
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https://math.stackexchange.com/questions/74677/covariance-of-increasing-functions – Oct 04 '17 at 23:03
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Also look up "FKG inequality". – Robert Israel Oct 05 '17 at 00:01

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