Chapter 9 - Distribution and Density Functions

Abstract

This chapter focuses on distribution and density functions. The probability distribution induced by a real-valued random variable X characterizes the random variable in a manner which is sufficient for many purposes. The probability distributions for simple, and most elementary, random variables are easy to describe and to visualize, as they concentrate probability mass at those points on the real line that represent possible values of the random variable. However, for more complicated distributions it is necessary to employ more sophisticated means of description. In any case, it is highly desirable to have analytical descriptions. The chapter discusses analytical tools for describing the probability distribution induced on the real line by a single, real-valued random variable. The chapter reviews the probability distribution function and a cumulative distribution function. Several examples of probability distributions are discussed that play very important roles in a variety of applications. One of the most widely encountered continuous probability distributions is the normal distribution.