An important quantity in a statistical analysis is the so-called covariance.

Consider the set $\{X_i\}$ of $n$ stochastic variables (not necessarily uncorrelated) with the multivariate PDF $P(x_1,\dots,x_n)$. The covariance of two of the stochastic variables, $X_i$ and $X_j$, is defined as follows $$\begin{align} \mathrm{Cov}(X_i,\,X_j) & = \langle (x_i-\langle x_i\rangle)(x_j-\langle x_j\rangle)\rangle \tag{6}\\ &=\int\cdots\int (x_i-\langle x_i\rangle)(x_j-\langle x_j\rangle)P(x_1,\dots,x_n)\,dx_1\dots dx_n, \tag{7} \end{align}$$ with $$\begin{equation*} \langle x_i\rangle = \int\cdots\int x_i P(x_1,\dots,x_n)\,dx_1\dots dx_n. \end{equation*}$$