Chi AU and Judy TAM in [1] and Samia WAHED and M.Masoom ALI in [2] compared the method of using the Dirac generalized function [3], [4] with the conventional Change of Variable Technique of transformed continuous random variables for several distributions. In the present article, we have applied the concept of generalized probability density function based on the Heaviside and the Dirac generalized functions for transformed random variables to obtain the distributions of several transformed discrete and continuous random variables. Moreover, we give a theorem for obtaining the joint distribution of a system of transformed continuous random variables and some of its applications.