I am reading this Covariance notes and it has the following explanation:
$$cov(X, Y) = \langle(X-\mu_X)(Y-\mu_Y)\rangle$$ $$=\langle X Y\rangle - \mu_X\mu_Y$$
where $\mu_X = \langle X \rangle, \mu_Y = \langle Y \rangle$ are the respective means, which can be written as:
$$cov(X, Y) = \sum\limits_{i=1}^N\frac{(x_i-\bar{x})(y_i-\bar{y})}{N}$$
As a result $$\langle XY \rangle - \langle X \rangle\langle Y \rangle = \sum\limits_{i=1}^N\frac{(x_i-\bar{x})(y_i-\bar{y})}{N}$$
What is $\langle X \rangle$?