Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

APPENDICES

INTRODUCTION TO APPENDICES

In the following appendices, we provide some background material that the reader might find useful as a review of several topics needed for the various chapters. Of course, most of this information can be found in other textbooks used in undergraduate engineering courses (such as the review of frequency-domain transforms), but it is included here so that the book is reasonably self-contained.

• Appendix A. Summaries of all the univariate random variables described in Chapter 3 are included for ease of reference. Each summary provides expressions for the probability density function (pdf), cumulative distribution function (cdf), moments, the characteristic function, and entropy, as well as example plots of each distribution (showing the mean and width μX ± σX). The random variables are organized alphabetically and with separate sections for continuous and discrete distributions.
• Appendix B. Continuity, boundedness, and various properties of functions are covered. We also include specific functions that are used throughout the book and provide example plots to illustrate their behavior. Nearly all of these functions arise because of the wide range of distributions in Chapter 3 and the need to describe the pdf, cdf, moments, and entropy in concise functional forms.
• Appendix C. Properties and transform pairs for the following frequency-domain transforms are summarized: (i) Laplace transform, (ii) continuous-time Fourier transform, (iii) z-transform, ...