# Covariance

A measure of the joint variability of two variables, cf: variance. Whereas the variance of a single random variable is the expectation of the square of the deviations from the mean, the covariance of X and Y is the expectation of the product of their deviations from the mean:

Cov(X,Y ) = E[(X −E[X])(Y −(E[Y ]))] = E[XY]−E[X]E[Y]

If the covariance is 0, X and Y are said to be uncorrelated. if X and Y are independent, the covariance will necessarily be zero, but the converse is not true. With multiple variables, their covariances may be expressed in a covariance matrix.