Covariance

The elements of such a correlation matrix do not have asymptotic variances and covariances of the form (1.2), even if S has a Wishart distribution.

Consequently, it can be shown that a covariance of two binary variables measures the extent to which the observed joint distribution of these variables differs from their expected joint distribution under the assumption that they are statistically independent.

The covariance of X and Y is the expected value of the product of two random variables, X − E(X) and Y − E(Y).[…]If two random variables tend to act like opposites, one is high when the other is low and vice versa, then the covariance will be negative. If two random variables tend to be high and low at the same time, then the covariance will be positive. In fact, the covariance measures the extent of a linear relationship between the two random variables.

As we will see in Chapter 8, we see both covariance and contravariance throughout the Java Collections. They largely exist to ensure that the generics just “do the right thing” and behave in a manner that should not surprise the developer.