Probability, random variables, and stochastic processes
Probability, random variables and stochastic processes was designed for students who are pursuing senior or graduate level courses, in probability. Those in the disciplines of mathematics physics, and electrical engineering will find this book useful.the authors have comprehensively covered the fundamental principles, and have demonstrated their usage by incorporating examples of basic applications. This edition has been thoroughly revised and updated, and has a co-author too. About 30% of the material is new, with a large number of additional examples which will help students understand the theory better. The design of the textbook has undergone some changes to make the flow of the content smoother.the first part of probability, random variables and stochastic processes contains eight chapters. The third chapter, titled repeated trials, contains an new section on bernoulli's theorem. In the chapter, the concept of a random variable, students will be able to learn about different probability distributions. The fifth and sixth chapters have new, and have rewritten examples. The chapter on statistics has a new section, which is dedicated to parameter estimation. The second part of this book focusses on stochastic processes, and has new sections on poisson processes. Two brand new chapters, focussing on markov chains and processes and queueing theory, have also been included in this edition.the fourth edition of the book, published by tata mcgraw hill education in 2002, is available in paperback. Key features: this classic book is used as a textbook across the world.
Why Read This Book
You should read this book if you need a rigorous yet application-minded foundation in probability and stochastic processes for signal-processing work: you will learn how probability theory underpins random signals, spectral analysis, and filtering, with many worked examples tying theory to engineering practice. The Papoulis & Pillai presentation balances mathematical depth and intuition, making it a go-to reference when you must move from formulas to real DSP reasoning.
Who Will Benefit
Ideal for senior undergraduate or graduate electrical engineers, signal-processing and communications students, and practicing engineers who need a solid mathematical foundation for DSP, radar, audio, or communications work.
Level: Advanced — Prerequisites: Single-variable and multivariable calculus, basic linear algebra, and introductory signals & systems (Fourier transforms, LTI systems); prior exposure to basic probability concepts is helpful but not strictly required.
Key Takeaways
- Apply axiomatic probability and conditional methods to model uncertainty in signals and systems
- Characterize and manipulate single and multivariate random variables using distributions, moments, and transforms
- Use characteristic functions, moment-generating techniques, and limit theorems to analyze sums and functions of random variables
- Analyze stochastic processes: stationarity, ergodicity, autocorrelation, and power spectral density for signal analysis
- Design and assess linear systems driven by random inputs, including spectral filtering and random response computation
- Model and analyze Markov and renewal processes and apply probabilistic tools to communications, radar, and detection problems
Topics Covered
- 1. Axioms of Probability and Combinatorial Methods
- 2. Conditional Probability, Independence and Bayes' Theorem
- 3. Random Variables and Their Distribution Functions
- 4. Expectation, Moments, and Inequalities
- 5. Functions of a Random Variable and Transformation Techniques
- 6. Joint Distributions, Conditional Distributions and Order Statistics
- 7. Characteristic Functions and Moment-Generating Methods
- 8. Limit Theorems: Laws of Large Numbers and Central Limit Theorem
- 9. Introduction to Stochastic Processes and Classification
- 10. Stationary Processes, Ergodicity, and Correlation Functions
- 11. Spectral Representation and Power Spectral Density
- 12. Linear Systems with Random Inputs and Filtering of Random Processes
- 13. Markov Chains, Renewal Processes and Applications
- 14. Selected Applications to Communications, Radar, and Signal Detection
How It Compares
Covers similar ground to Grimmett & Stirzaker's Probability and Random Processes but is more tailored to engineering applications and signal-processing examples; Ross's A First Course in Probability is more introductory, while Papoulis & Pillai goes deeper into stochastic processes relevant to DSP.
