Probability, Random Variables and Stochastic Processes with Errata Sheet
The fourth edition of Probability, Random Variables and Stochastic Processes has been updated significantly from the previous edition, and it now includes co-author S. Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material--this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics.
Why Read This Book
You should read this book to gain a rigorous, compact foundation in probability and stochastic processes that directly supports DSP tasks such as spectral analysis, random-signal modeling, and linear-system responses to noise. The text ties theory to engineering-relevant examples so you can apply limit theorems, correlation/spectrum relationships, and stochastic-process tools to real DSP problems.
Who Will Benefit
Senior undergraduates, graduate students, and practicing DSP/communications engineers who need a rigorous mathematical foundation in probability and stochastic processes for analysis, modeling, and algorithm design.
Level: Advanced — Prerequisites: Single-variable and multivariable calculus, basic linear algebra, and familiarity with deterministic signals and linear systems; basic exposure to probability is helpful but not mandatory.
Key Takeaways
- Formulate and manipulate probability measures, random variables, and joint distributions for engineering problems.
- Analyze stochastic processes including stationarity, ergodicity, and wide-sense properties used in DSP.
- Compute and relate autocorrelation functions and power spectral densities (Wiener-Khinchin relationships).
- Apply limit theorems (law of large numbers, central limit theorem) to understand estimation and averaging behavior.
- Model and analyze common processes (Gaussian, Poisson, Markov) and their behavior through linear systems.
Topics Covered
- Fundamental Concepts of Probability
- Random Variables and Distribution Functions
- Functions of Random Variables and Transform Methods
- Moments, Characteristic and Generating Functions
- Convergence of Sequences of Random Variables; Limit Theorems
- Multiple Random Variables and Joint Distributions
- Introduction to Stochastic Processes
- Stationarity, Ergodicity, and Correlation Functions
- Power Spectral Density and Spectral Representation
- Linear Systems Excited by Random Processes
- Gaussian Processes and Applications
- Markov Chains and Continuous-Time Markov Processes
- Point Processes and Renewal Theory
- Applications to Communications and Signal Analysis
How It Compares
Covers similar ground to Leon-Garcia's 'Probability and Random Processes for Electrical Engineering' but is generally more concise and mathematically rigorous; Leon-Garcia is often more example-driven and accessible for beginners.
