Introduction to Probability for Computing

This chapter is a very brief introduction to the wonderful world of transforms. Transforms come in many varieties. There are z-transforms, moment-generating functions, characteristic functions, Fourier transforms, Laplace transforms, and more. All are very similar in their function. In this chapter, we will study z-transforms, a variant particularly well suited to common discrete random variables. In Chapter 11, we will study Laplace transforms, a variant ideally suited to common continuous random variables.