On the Arithmetic Means and Variances of Products and Ratios of Random Variables

Summary

Frequently occuring functions of random variables, that arise in the area of applied statistics, are the Product and Ratio of pairs of not necessarily independent variates. As is the case in much statistical work, in practice, attempts to understand the underlying processes usually begin with the consideration of the mean and variance. Exact expressions are given for the mean and variance of a ratio of random variables under mildly restrictive conditions. In addition approximation results are obtained which, it is argued, may be of practical use in many of the cases, including normality, where the restrictions are violated.