Correlation

In statistics, correlation is a measure of how well there’s a statistical relationship within bivariate data. We sometimes use the Pearson correlation coefficient as this metric.

We refer to the $jk$th joint moment of $X$ and $Y$ where $j=k=1$ as the correlation of $X$ and $Y$, i.e.,:

$$E(XY)={\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }xy{f}_{X,Y}(x,y)dxdy$$ $$E(XY)=\sum _i\sum _n{x}_i{y}_n{p}_{X,Y}(x_i,y_n)$$

If $E(XY)=0$, then we say that $X$ and $Y$ are orthogonal.