This research considers a generalized version of the univariate change-of-variable technique for transforming random variables. Extending a theorem from Casella and Berger (1990) for K-to-1 transformations, more general transformations are considered. Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest. The research includes an implementation of the theorem in a symbolic algebra computer language that automates the technique. (Ph.D. student on the project: Andy Glen).