Probability and random processes : with applications to signal processing and communications / Scott L. Miller, Donald Childers.

Includes bibliographical references and index.

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 EventsSection 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 Variable3.4.3 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 FunctionsSection 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 Functions4.10 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.