Abstract
Most authors of probability and statistics books introduce the definition of a joint-distribution function to prove certain properties involving moment-generating functions for distribution functions of independently distributed chance variables.
The purpose of this paper is to show that some of these properties can be established without using the definition of a joint-distribution function.
First, some properties involving sets and independent chance variables will be established. These arguments will then be used to obtain the distribution function for the sum of two independent chance variables.
