Probability, Statistics, and Random Processes For Electrical Engineering, 3rd edition

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