Description: 1. Probability Models in Electrical and Computer Engineering 1.1 Mathematical Models as Tools in Analysis and Design 1.2 Deterministic Models 1.3 Probability Models 1.4 A Detailed Example: A Packet Voice Transmission System 1.5 Other Examples 1.6 Overview of Book Summary Problems 2. Basic Concepts of Probability Theory 2.1 Specifying Random Experiments 2.2 The Axioms of Probability 2.3 Computing Probabilities Using Counting Methods 2.4 Conditional Probability 2.5 Independence of Events 2.6 Sequential Experiments 2.7 Synthesizing Randomness: Random Number Generators 2.8 Fine Points: Event Classes 2.9 Fine Points: Probabilities of Sequences of Events Summary Problems 3. Discrete Random Variables 3.1 The Notion of a Random Variable 3.2 Discrete Random Variables and Probability Mass Function 3.3 Expected Value and Moments of Discrete Random Variable 3.4 Conditional Probability Mass Function 3.5 Important Discrete Random Variables 3.6 Generation of Discrete Random Variables Summary Problems 4. One Random Variable 4.1 The Cumulative Distribution Function 4.2 The Probability Density Function 4.3 The Expected Value of X 4.4 Important Continuous Random Variables 4.5 Functions of a Random Variable 4.6 The Markov and Chebyshev Inequalities 4.7 Transform Methods 4.8 Basic Reliability Calculations 4.9 Computer Methods for Generating Random Variables 4.10 Entropy Summary Problems 5. Pairs of Random Variables 5.1 Two Random Variables 5.2 Pairs of Discrete Random Variables 5.3 The Joint cdf of X and Y 5.4 The Joint pdf of Two Continuous Random Variables 5.5 Independence of Two Random Variables 5.6 Joint Moments and Expected Values of a Function of Two Random Variables 5.7 Conditional Probability and Conditional Expectation 5.8 Functions of Two Random Variables 5.9 Pairs of Jointly Gaussian Random Variables 5.10 Generating Independent Gaussian Random Variables Summary Problems 6. Vector Random Variables 6.1 Vector Random Variables 6.2 Functions of Several Random Variables 6.3 Expected Values of Vector Random Variables 6.4 Jointly Gaussian Random Vectors 6.5 Estimation of Random Variables 6.6 Generating Correlated Vector Random Variables Summary Problems 7. Sums of Random Variables and Long-Term Averages 7.1 Sums of Random Variables 7.2 The Sample Mean and the Laws of Large Numbers Weak Law of Large Numbers Strong Law of Large Numbers 7.3 The Central Limit Theorem Central Limit Theorem 7.4 Convergence of Sequences of Random Variables 7.5 Long-Term Arrival Rates and Associated Averages 7.6 Calculating Distribution''s Using the Discrete Fourier Transform Summary Problems 8. Statistics 8.1 Samples and Sampling Distributions 8.2 Parameter Estimation 8.3 Maximum Likelihood Estimation 8.4 Confidence Intervals 8.5 Hypothesis Testing 8.6 Bayesian Decision Methods 8.7 Testing the Fit of a Distribution to Data Summary Problems 9. Random Processes 9.1 Definition of a Random Process 9.2 Specifying a Random Process 9.3 Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk 9.4 Poisson and Associated Random Processes 9.5 Gaussian Random Processes,Wiener Process and Brownian Motion 9.6 Stationary Random Processes 9.7 Continuity, Derivatives, and Integrals of Random Processes 9.8 Time Averages of Random Processes and Ergodic Theorems 9.9 Fourier Series and Karhunen-Loeve Expansion 9.10 Generating Random Processes Summary Problems 10. Analysis and Processing of Random Signals 10.1 Power Spectral Density 10.2 Response of Linear Systems to Random Signals 10.3 Bandlimited Random Processes 10.4 Optimum Linear Systems 10.5 The Kalman Filter 10.6 Estimating the Power Spectral Density 10.7 Numerical Techniques for Processing Random Signals Summary Problems 11. Markov Chains 11.1 Markov Processes 11.2 Discrete-Time Markov Chains 11.3 Classes of States, Recurrence Properties, and Limiting Probabilities 11.4 Continuous-Time Markov Chains 11.5 Time-Reversed Markov Chains 11.6 Numerical Techniques for Markov Chains Summary Problems 12. Introduction to Queueing Theory 12.1 The Elements of a Queueing System 12.2 Little''s Formula 12.3 The M/M/1 Queue 12.4 Multi-Server Systems: M/M/c, M/M/c/c,And 12.5 Finite-Source Queueing Systems 12.6 M/G/1 Queueing Systems 12.7 M/G/1 Analysis Using Embedded Markov Chains 12.8 Burke''s Theorem: Departures From M/M/c Systems 12.9 Networks of Queues: Jackson''s Theorem 12.10 Simulation and Data Analysis of Queueing Systems Summary Problems Appendices A. Mathematical Tables B. Tables of Fourier Transforms C. Matrices and Linear Algebra

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