TITLE: covariance of increasing functions
QUESTION [5 upvotes]: Suppose $f$ and $g$ are monotonically increasing, and bounded, and let $X$ be a random variable. I want to show $f$, $g$ have positive covariance.  I tried to compute it directly but I am not getting anything useful

REPLY [7 votes]: I think you can consider $\mathbb{E}[(f(X)-f(Y))(g(X)-g(Y))]$ where $X$ and $Y$ are i.i.d.