For the general case of jointly distributed random variablesxandy, Goodman [3] derives the exact variance of the productxy.For the special case wherexandyare 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 productsxyanduv, and sketch several specializations and applications.