Consider the following probability distribution function:
\begin{equation} p(x,y)=\frac{x}{\pi}e^{\frac{-x^2}{4} (5+3sin(2y))} \end{equation}
Obviously integrating this equation to find the expectations E(XY) and E(X)E(Y) and seeing if they equal each other will be very difficult.
How do I, then, figure out whether the random variables X and Y are correlated or not?