CHAPTER 5 - Absolutely Continuous Distributions

Abstract

This chapter presents the absolutely continuous distributions. The discrete distributions and the continuous distributions are two small disjoint classes of distributions. They are easier to handle than the other distributions. There are many distribution functions that are not discrete and are not continuous. The distribution functions of the continuous random variables are only a small part of those distributions with continuous distribution functions. If the random variables have a joint absolutely continuous distribution, then it can be easily shown whether they are independent. Conditional distributions are needed in much work in probability and statistics. If a joint density of a finite set of random variables is given, then the joint density of a certain number of random variables can be found if the extraneous variables are integrated out.