Front Cover -- Probability and Random Processes: With Applications to Signal Processingand Communications -- Copyright -- 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 Basic Combinatorics -- 2.6 Bayes's Theorem -- 2.7 Independence -- 2.8 Discrete Random Variables -- 2.9 Engineering Application-An Optical Communication System -- Exercises -- Section 2.1: Experiments, Sample Spaces, and Events -- Section 2.2: Axioms of Probability -- Section 2.3: Assigning Probabilities -- Section 2.4: Joint and Conditional Probabilities -- Section 2.5: Basic Combinatorics -- Section 2.6: Bayes's Theorem -- Section 2.7: Independence -- Section 2.8: Discrete Random Variables -- Miscellaneous Problems -- MATLAB Exercises -- 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 -- 3.4.1 Uniform Random Variable -- 3.4.2 Exponential Random Variable -- 3.4.3 Laplace Random Variable -- 3.4.4 Gamma Random Variable -- 3.4.5 Erlang Random Variable -- 3.4.6 Chi-Squared Random Variable -- 3.4.7 Rayleigh Random Variable -- 3.4.8 Rician Random Variable -- 3.4.9 Cauchy Random Variable -- 3.5 Conditional Distribution and Density Functions -- 3.6 Engineering Application: Reliability and Failure Rates -- Exercises -- Section 3.1: The Cumulative Distribution Function -- Section 3.2: The Probability Density Function -- Section 3.3: The Gaussian Random Variable -- Section 3.4: Other Important Random Variables.

Section 3.5: Conditional Distribution and Density Functions -- Section 3.6: Reliability and Failure Rates -- Miscellaneous Exercises -- MATLAB Exercises -- 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 -- 4.6.1 Monotonically Increasing Functions -- 4.6.2 Monotonically Decreasing Functions -- 4.6.3 Nonmonotonic Functions -- 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 -- Exercises -- Section 4.1: Expected Values of a Random Variable -- Section 4.2: Expected Values of Functions of a Random Variable -- Section 4.3: Moments -- Section 4.4: Central Moments -- Section 4.5: Conditional Expected Values -- Section 4.6: Transformations of Random Variables -- Section 4.7: Characteristic Functions -- Section 4.8: Probability-Generating Functions -- Section 4.9: Moment-Generating Functions -- Section 4.10: Evaluating Tail Probabilities -- Section 4.11: Scalar Quantization -- Section 4.12: Entropy and Source Coding -- Miscellaneous Exercises -- MATLAB Exercises -- 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 -- Exercises -- Section 5.1: Joint CDFs -- Section 5.2: Joint PDFs -- Section 5.3: Joint PMFs -- Section 5.4: Conditional Distribution, Density and Mass Functions -- Section 5.5: Expected Values Involving Pairs of Random Variables -- Section 5.6: Independent Random Variables -- Section 5.7: Joint Gaussian Random Variables -- Section 5.8: Joint Characteristic and Related Functions -- Section 5.9: Transformations of Pairs of Random Variables -- Section 5.10: Complex Random Variables -- Section 5.11: Mutual Information, Channel Capacity, and Channel Coding -- Miscellaneous Problems -- MATLAB Exercises -- 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 -- 6.4.1 Linear Transformations -- 6.4.2 Quadratic Transformations of Gaussian Random Vectors -- 6.4.3 Order Statistics -- 6.4.4 Coordinate Systems in Three Dimensions -- 6.5 Estimation and Detection -- 6.5.1 Maximum a Posteriori Estimation -- 6.5.2 Maximum Likelihood Estimation -- 6.5.3 Minimum Mean Square Error Estimation -- 6.6 Engineering Application: Linear Prediction of Speech -- Exercises -- Section 6.1: Joint and Conditional PMFs, CDFs, and PDFs -- Section 6.2: Expectations Involving Multiple Random Variables -- Section 6.3: Gaussian Random Variables in Muliple Dimensions -- Section 6.4: Transformations Involving Multiple Random Variables -- Section 6.5: Estimation and Detection -- Miscellaneous Exercises -- MATLAB Exercises -- Chapter 7: Random Sums and Sequences -- 7.1 Independent and Identically Distributed Random Variables.

7.1.1 Estimating the Mean of IID Random Variables -- 7.1.2 Estimating the Variance of IID Random Variables -- 7.1.3 Estimating the CDF of IID Random Variables -- 7.2 Convergence Modes of Random Sequences -- 7.2.1 Convergence Everywhere -- 7.2.2 Convergence Almost Everywhere -- 7.2.3 Convergence in Probability -- 7.2.4 Convergence in the Mean Square Sense -- 7.2.5 Convergence in Distribution -- 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 -- Exercises -- Section 7.1: IID Random Variables -- Section 7.2: Convergence Modes of Random Sequences -- Section 7.3: The Law of Large Numbers -- Section 7.4: The Central Limit Theorem -- Section 7.5: Confidence Intervals -- Section 7.6: Random Sums of Random Variables -- Miscellaneous Exercises -- MATLAB Exercises -- 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 -- Exercises -- Section 8.2: Mathematical Tools for Studying Random Processes -- Section 8.3: Stationary and Ergodic Random Processes -- Section 8.4: Properties of the Autocorrelation Function -- Section 8.5: Gaussian Random Processes -- Section 8.6: Poisson Processes -- Section 8.7: Shot Noise in a p-n Junction Diode -- Miscellaneous Exercises -- MATLAB Exercises -- 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 -- Exercises -- Section 9.1: Definition and Examples of Markov Processes -- Section 9.2: Calculating Transition and State Probabilities -- Section 9.3: Characterization of Markov Chains -- Section 9.4: Continuous Time Markov Processes -- MATLAB Exercises -- Chapter 10: Power Spectral Density -- 10.1 Definition of PSD -- 10.2 The Wiener-Khintchine-Einstein Theorem -- 10.3 Bandwidth of a Random Process -- 10.4 Spectral Estimation -- 10.4.1 Non-parametric Spectral Estimation -- 10.4.2 Parametric Spectral Estimation -- 10.5 Thermal Noise -- 10.6 Engineering Application: PSDs of Digital Modulation Formats -- Exercises -- Section 10.1: Definition of PSD -- Section 10.2: Wiener-Khintchine-Einstein Theorem -- Section 10.3: Bandwidth of a Random Process -- Section 10.4: Spectral Estimation -- Section 10.5: Thermal Noise -- MATLAB Exercises -- 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 -- Exercises -- Section 11.1: Continuous Time Linear Systems -- Section 11.2: Discrete-Time Systems -- Section 11.3: Noise Equivalent Bandwidth -- Section 11.4: Signal-to-Noise Ratios -- Section 11.5: The Matched Filter -- Section 11.6: The Wiener Filter -- Sections 11.7 and 11.8: Narrowband Random Processes and Complex Envelopes -- MATLAB Exercises -- Chapter 12: Simulation Techniques -- 12.1 Computer Generation of Random Variables -- 12.1.1 Binary Pseudorandom Number Generators -- 12.1.2 Nonbinary Pseudorandom Number Generators.

12.1.3 Generation of Random Numbers from a Specified Distribution.