On the Exact Covariance of Products of Random Variables

Abstract For the general case of jointly distributed random variables x and y, Goodman 3 derives the exact variance of the product xy. For the special case where x and y are stochastically independent, he provides a simpler expression for the exact variance. We offer a weaker set of assumptions which suffices to yield the simpler expression. We then extend Goodman's analysis to present the exact covariance of two products xy and uv, and sketch several specializations and applications.