Properties Relating Independent Chance Variables, Distribution Functions, and Moment-generating Functions

Abstract

<p>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.</p> <p>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.</p> <p>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.</p>