- Cover Image
- Table of Contents
- Title
- Copyright
- Preface
- Chapter 1. Introduction
- Chapter 2. Introduction to Probability Theory
- Chapter 3. Random Variables, Distributions, and Density Functions
- Chapter 4. Operations on a Single Random Variable
- 4.1 Expected Value of a Random Variable
- 4.2 Expected Values of Functions of Random Variables
- 4.3 Moments
- 4.4 Central Moments
- 4.5 Conditional Expected Values
- 4.6 Transformations of Random Variables
- 4.7 Characteristic Functions
- 4.8 Probability-Generating Functions
- 4.9 Moment-Generating Functions
- 4.10 Evaluating Tail Probabilities
- 4.11 Engineering Application—Scalar Quantization
- 4.12 Engineering Application—Entropy and Source Coding
- Chapter 5. Pairs of Random Variables
- 5.1 Joint Cumulative Distribution Functions
- 5.2 Joint Probability Density Functions
- 5.3 Joint Probability Mass Functions
- 5.4 Conditional Distribution, Density, and Mass Functions
- 5.5 Expected Values Involving Pairs of Random Variables
- 5.6 Independent Random Variables
- 5.7 Jointly Gaussian Random Variables
- 5.8 Joint Characteristic and Related Functions
- 5.9 Transformations of Pairs of Random Variables
- 5.10 Complex Random Variables
- 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding
- Chapter 6. Multiple Random Variables
- Chapter 7. Random Sums and Sequences
- Chapter 8. Random Processes
- 8.1 Definition and Classification of Processes
- 8.2 Mathematical Tools for Studying Random Processes
- 8.3 Stationary and Ergodic Random Processes
- 8.4 Properties of the Autocorrelation Function
- 8.5 Gaussian Random Processes
- 8.6 Poisson Processes
- 8.7 Engineering Application—Shot Noise in a p–n Junction Diode
- Chapter 9. Markov Processes
- 9.1 Definition and Examples of Markov Processes
- 9.2 Calculating Transition and State Probabilities in Markov Chains
- 9.3 Characterization of Markov Chains
- 9.4 Continuous Time Markov Processes
- 9.5 Engineering Application: A Computer Communication Network
- 9.6 Engineering Application: A Telephone Exchange
- Chapter 10. Power Spectral Density
- Chapter 11. Random Processes in Linear Systems
- 11.1 Continuous Time Linear Systems
- 11.2 Discrete-Time Linear Systems
- 11.3 Noise Equivalent Bandwidth
- 11.4 Signal-to-Noise Ratios
- 11.5 The Matched Filter
- 11.6 The Wiener Filter
- 11.7 Bandlimited and Narrowband Random Processes
- 11.8 Complex Envelopes
- 11.9 Engineering Application: An Analog Communication System
- Chapter 12. Simulation Techniques
- APPENDIX A. Review of Set Theory
- APPENDIX B. Review of Linear Algebra
- APPENDIX C. Review of Signals and Systems
- APPENDIX D. Summary of Common Random Variables
- APPENDIX E. Mathematical Tables
- APPENDIX F. Numerical Methods for Evaluating the Q-Function
Probability and Random Processes
With Applications to Signal Processing and Communications
Edition 2
Scott L. Miller
Professor, Department of Electrical and Computer Engineering, Texas A&M University
Donald Childers
Professor Emeritus, Department of Electrical and Computer Engineering, University of Florida
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