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Let $X$ and $Y$ two random variables such that $X^2,Y^2$ have an expectation. We define the correlation between $X$ and $Y$ by $$\operatorname{Corr}(X,Y):=\frac{E((X-EX)(Y-EY))}{\sqrt{E(X^2)E(Y^2)}}$$ when $EX^2EY^2\neq 0$, and $0$ otherwise.

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