Front Cover -- Probability and Random Processes -- Copyright Page -- Contents -- Preface -- Chapter 1. Introduction -- 1.1 A Speech Recognition System -- 1.2 A Radar System -- 1.3 A Communication Network -- Chapter 2. Introduction to Probability Theory -- 2.1 Experiments, Sample Spaces, and Events -- 2.2 Axioms of Probability -- 2.3 Assigning Probabilities -- 2.4 Joint and Conditional Probabilities -- 2.5 Bayes's Theorem -- 2.6 Independence -- 2.7 Discrete Random Variables -- 2.8 Engineering Application: An Optical Communication System -- Chapter 3. Random Variables, Distributions, and Density Functions -- 3.1 The Cumulative Distribution Function -- 3.2 The Probability Density Function -- 3.3 The Gaussian Random Variable -- 3.4 Other Important Random Variables -- 3.5 Conditional Distribution and Density Functions -- 3.6 Engineering Application: Reliability and Failure Rates -- 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 -- 6.1 Joint and Conditional PMFs, CDFs, and PDFs -- 6.2 Expectations Involving Multiple Random Variables -- 6.3 Gaussian Random Variables in Multiple Dimensions -- 6.4 Transformations Involving Multiple Random Variables -- 6.5 Engineering Application: Linear Prediction of Speech -- Chapter 7. Random Sequences and Series -- 7.1 Independent and Identically Distributed Random Variables -- 7.2 Convergence Modes of Random Sequences -- 7.3 The Law of Large Numbers -- 7.4 The Central Limit Theorem -- 7.5 Confidence Intervals -- 7.6 Random Sums of Random Variables -- 7.7 Engineering Application: A Radar System -- 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 -- 10.1 Definition of Power Spectral Density -- 10.2 The Wiener-Khintchine-Einstein Theorem -- 10.3 Bandwidth of a Random Process -- 10.4 Spectral Estimation -- 10.5 Thermal Noise -- 10.6 Engineering Application: PSDs of Digital Modulation Formats -- 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: Noise in an Analog Communications System -- Chapter 12. Simulation Techniques -- 12.1 Computer Generation of Random Variables -- 12.2 Generation of Random Processes -- 12.3 Simulation of Rare Events -- 12.4 Engineering Application: Simulation of a Coded Digital Communication System -- Appendices -- A Review of Set Theory -- B Review of Linear Algebra -- C Review of Signals and Systems -- D Summary of Common Random Variables -- E Mathematical Tables -- F Numerical Methods for Evaluating the Q-Function -- Index.