An application of mutual information in mathematical statistics education

Abstract

In mathematical statistics education, we can use mutual information as a tool for evaluating the degree of dependency between two random variables. The ordinary correlation coefficient provides information only on linear dependency, not on nonlinear relationship between two random variables if any. In this paper as a measure of the degree of dependency between random variables, we suggest the use of symmetric uncertainty and <TEX>${\lambda}$</TEX> which are defined in terms of mutual information. They can be also considered as generalized correlation coefficients for both linear and non-linear dependence of random variables.