Deriving the Probability Density for Sums of Uniform Random Variables

A simple procedure for deriving the probability density function (pdf) for sums of uniformly distributed random variables is offered. This method is suited to introductory courses in probability and mathematical statistics. In our experience, deriving and working with the pdf for sums of random variables facilitates an understanding of the convergence properties of the density of such sums and motivates consideration of other algebraic manipulation for random variables.