Fundamentals of Applied Probability and Random Processes, 2nd Edition

Chapter 7

Transform Methods

Abstract

This chapter discusses transform methods that are useful in computing moments of random variables. In particular, it discusses the characteristic function, the z-transform of the probability mass functions of discrete random variables and the s-transform of the probability distribution functions of continuous random variables.

Keywords

Characteristic function

z-transform

s-transform

moment generating functions

7.1 Introduction

Different types of transforms are used in science and engineering. These include the z-transform, Laplace transform, and Fourier transform. One of the reasons for their popularity is that when they are introduced into the solution of many problems, the calculations become greatly ...