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Introduction to Probability, Statistics, and Random Processes
This book introduces students to probability, statistics, and stochastic processes. It can be used by both students and practitioners in engineering, various sciences, finance, and other related fields. It provides a clear and intuitive approach to these topics while maintaining mathematical accuracy.
The book covers:
• Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods
• Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities
• Limit theorems and convergence
• Introduction to Bayesian and classical statistics
• Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion
• Simulation using MATLAB and R (online chapters)
The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications—such as engineering, finance, everyday life, etc.—are included to aid in motivating the subject. The digital version of the book, as well as additional materials such as videos, is available at probabilitycourse.com.
The book covers:
• Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods
• Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities
• Limit theorems and convergence
• Introduction to Bayesian and classical statistics
• Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion
• Simulation using MATLAB and R (online chapters)
The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications—such as engineering, finance, everyday life, etc.—are included to aid in motivating the subject. The digital version of the book, as well as additional materials such as videos, is available at probabilitycourse.com.
746 pages, Paperback
First published August 24, 2014
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Displaying 1 - 5 of 5 reviews
August 18, 2023
Good overview of non measure theoretic probability. Random variables, functions and processes (though primarily discrete). Book has a computer science / electrical engineering bent.
July 12, 2025
I am very disappointed with this book. While it has several strengths—especially as an introduction to probability theory—it also has massive weaknesses. It is likely the best beginner-friendly textbook on probability theory available today. However, the two chapters on statistics are bad.
The first few chapters of the book are excellent and raised my expectations for the rest. Unfortunately, the later chapters did not live up to that standard, which made my disappointment even sharper.
The author is a skilled teacher who explains complex ideas clearly and uses strong examples to support his points. He makes an effort to avoid heavy abstraction, aiming not to overwhelm the reader. Even so, many parts of the chapters on probability theory and random processes feel overly theoretical, with little practical relevance. That made it hard for me to stay motivated.
I would cut some of the theorem proofs from the chapters on probability theory and random processes. Instead, the book would benefit from more examples that closely reflect real-world problems.
The two chapters on statistics are extremely weak. They gave me the impression that the author looks down on statistics, treating it as too primitive compared to probability theory.
The following paragraph is a verbatim quote from the book.
Based on the above discussion, we should accept H0. However, it is often recommended to say "we failed to reject H0" instead of saying "we are accepting H0." The reason is that we have not really proved that H0 is true. In fact, all we know is that the result of our experiment was not statistically contradictory to H0. Nevertheless, we will not worry about this terminology in this book.
This approach is flawed and harmful. This terminology is what the teachers and students should be concerned about. In practice, there is a big difference between failing to reject a hypothesis and simply accepting it. Recognizing this difference is a core skill for any data analyst. It is much more important than being able to solve complex integrals analytically or write long proofs of theorems.
The book does not even mention bootstrapping as an alternative to traditional hypothesis testing based on the normal distribution. In the linear regression section, the author spends several pages on matrix operations but skips over practical issues, like how to identify which explanatory variables matter. The chapter on Bayesian statistics feels weak, unclear, and rushed.
The author could have at least recommended additional reading on statistics and regression. But he did not make that effort. As a result, many readers may walk away with a distorted view of statistics. That is unfortunate, because statistics is often the most useful branch of mathematics for practitioners. It helps solve real-world problems across many fields.
The author promises that a semester-long course in calculus is enough to follow the book, and he delivers on that. The book contains many integrals, but they are fairly simple. Some of the examples also have basic infinite series and differentiation. Several sections do require solid skills in matrix operations.
The student’s guide provides solutions only for exercises with odd numbers. It is a book's drawback. Without answers for even-numbered problems, readers may lose motivation to attempt them since they cannot verify their solutions.
The first few chapters of the book are excellent and raised my expectations for the rest. Unfortunately, the later chapters did not live up to that standard, which made my disappointment even sharper.
The author is a skilled teacher who explains complex ideas clearly and uses strong examples to support his points. He makes an effort to avoid heavy abstraction, aiming not to overwhelm the reader. Even so, many parts of the chapters on probability theory and random processes feel overly theoretical, with little practical relevance. That made it hard for me to stay motivated.
I would cut some of the theorem proofs from the chapters on probability theory and random processes. Instead, the book would benefit from more examples that closely reflect real-world problems.
The two chapters on statistics are extremely weak. They gave me the impression that the author looks down on statistics, treating it as too primitive compared to probability theory.
The following paragraph is a verbatim quote from the book.
Based on the above discussion, we should accept H0. However, it is often recommended to say "we failed to reject H0" instead of saying "we are accepting H0." The reason is that we have not really proved that H0 is true. In fact, all we know is that the result of our experiment was not statistically contradictory to H0. Nevertheless, we will not worry about this terminology in this book.
This approach is flawed and harmful. This terminology is what the teachers and students should be concerned about. In practice, there is a big difference between failing to reject a hypothesis and simply accepting it. Recognizing this difference is a core skill for any data analyst. It is much more important than being able to solve complex integrals analytically or write long proofs of theorems.
The book does not even mention bootstrapping as an alternative to traditional hypothesis testing based on the normal distribution. In the linear regression section, the author spends several pages on matrix operations but skips over practical issues, like how to identify which explanatory variables matter. The chapter on Bayesian statistics feels weak, unclear, and rushed.
The author could have at least recommended additional reading on statistics and regression. But he did not make that effort. As a result, many readers may walk away with a distorted view of statistics. That is unfortunate, because statistics is often the most useful branch of mathematics for practitioners. It helps solve real-world problems across many fields.
The author promises that a semester-long course in calculus is enough to follow the book, and he delivers on that. The book contains many integrals, but they are fairly simple. Some of the examples also have basic infinite series and differentiation. Several sections do require solid skills in matrix operations.
The student’s guide provides solutions only for exercises with odd numbers. It is a book's drawback. Without answers for even-numbered problems, readers may lose motivation to attempt them since they cannot verify their solutions.
May 15, 2024
Best intro to probability book I've ever read. It's just the right mix of theory, exposition, and examples. Very quick read if you're already familiar with the material. Excellent worked examples. Unlike some more rudimentary books, this also covers a few advanced topics and gets at some practical use cases. The material is presented in a very logical and easy-to-follow order, such that if you read it end-to-end, you'll feel like almost everything is motivated. (Main exception possibly being MGFs/CFs, which I've never been really seen "motivation" for and whose origin/development I really don't know. Perhaps that's better covered by a differential equations book somewhere, as it seems to be closely related to the Fourier transform.)
I'm rereading it at the moment as review and I appreciate the layout and conciseness even more than I did before.
EDIT: After reading some other reviews, I wonder if this resonates with me due to my computer science background. YMMV
I'm rereading it at the moment as review and I appreciate the layout and conciseness even more than I did before.
EDIT: After reading some other reviews, I wonder if this resonates with me due to my computer science background. YMMV
September 21, 2023
It's generous of the author to build a website for everyone to read this book for free, although the site sucks. It can be served as a review, but I don't think readers should choose it as their first primary one, since so many things like Fourier transform are way too brief, and some important things lack expansion, like proof of CLT, I search it online, it is not complex at all.
January 3, 2025
I have had a wonderful time studying on the website platform, whose content is based on the book. With rigorous mathematical explanations, beautifully presented layouts, and instructive exercises and solutions, I believe this book (along with its online website version) is a great source for any undergraduate student who wants to study probability and statistics.
Displaying 1 - 5 of 5 reviews