Engineering & Transportation

Sorry, this item is not available in
Image not available for
Image not available

To view this video download Flash Player

Have one to sell? Sell yours here
Tell the Publisher!
I'd like to read this book on Kindle

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

Probability, Random Variables and Stochastic Processes [International Edition] [Paperback]

Athanasios Papoulis , S. Unnikrishna Pillai
3.3 out of 5 stars  See all reviews (47 customer reviews)

Available from these sellers.

Free Two-Day Shipping for College Students with Amazon Student


Amazon Price New from Used from
Hardcover --  
Paperback, International Edition --  
Unknown Binding --  
Engineering & Transportation Books
Discover books for all types of engineers, auto enthusiasts, and much more. Learn more

Book Description

January 1, 2002 0071226613 978-0071226615 4th
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.

Editorial Reviews Review

This text is a classic in probability, statistics, and estimation and in the application of these fields to modern engineering problems. Probability, Random Variables, and Stochastic Processes assumes a strong college mathematics background. The first half of the text develops the basic machinery of probability and statistics from first principles while the second half develops applications of the basic theory. Topics in the first section include probability distributions and densities, random variables and vectors, expectations, covariance, correlations, functions of random variables and vectors, and conditional distributions and densities. In this third edition of the text, the second half of the book has been substantially updated and expanded to include new or revised discussions of the following topics: mean square estimation, likelihood tests, maximum entropy methods, Monte Carlo techniques, spectral representations and estimation, sampling theory, bispectra and system identification, cyclostationary processes, deterministic signals in noise, and the Wiener and Kalman filters. Probability, Random Variables, and Stochastic Processes covers a remarkable density of material and the clarity of both presentation and notation make this book invaluable as a text and a reference. --This text refers to an out of print or unavailable edition of this title.

About the Author

S. Unnikrishna Pillai is a Professor of Electrical and Computer Engineering at Polytechnic Institute of NYU in Brooklyn, New York. His research interests include radar signal processing, blind identification, spectrum estimation, data recovery and wavform diversity. Dr. Pillai is the author of Array Signal Processign and co-author of Spectrum Estimation and system Identification, Prof. Papoulis’ Probability, Random Variables and Stochastic processes (Fourth edition), and Space Based Radar – Theory & Applications.

Product Details

  • Paperback: 852 pages
  • Publisher: McGraw-Hill Europe; 4th edition (January 1, 2002)
  • Language: English
  • ISBN-10: 0071226613
  • ISBN-13: 978-0071226615
  • Product Dimensions: 7.3 x 9.2 inches
  • Shipping Weight: 2.7 pounds
  • Average Customer Review: 3.3 out of 5 stars  See all reviews (47 customer reviews)
  • Amazon Best Sellers Rank: #660,842 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews
32 of 32 people found the following review helpful
5.0 out of 5 stars Found no substitute for a difficult subject July 21, 2013
Format:Paperback|Verified Purchase
When readers and students ask to me for a useable book for nonmathematicians to get into probability (or a probabilistic approach to statistics), before embarking into deeper problems, I suggest this book by the Late A. Papoulis. I even recommend it to mathematicians as their training often tends to make them spend too much time on limit theorems and very little on the actual "plumbing".
The treatment has no measure theory, cuts to the chase, and can be used as a desk reference. If you want measure theory, go spend some time reading Billingsley. A deep understanding of measure theory is not necessary for scientific and engineering applications; it is not necessary for those who do not want to work on theorems and technical proofs.
I've notice a few complaints in the comments section by people who felt frustrated by the treatment: do not pay attention to them. Ignore them. It the subject itself that is difficult, not this book. The book, in fact, is admirable and comprehensive given the current state of the art.
I am using this book as a benchmark while writing my own, but more advanced, textbook (on errors in use of statistical models). Anything derived and presented in Papoulis, I can skip. And when students ask me what they need as pre-requisite to attend my class or read my book, my answer is: Papoulis if you are a scientist, Varadhan if you are more abstract.
Was this review helpful to you?
33 of 36 people found the following review helpful
3.0 out of 5 stars Good book with the help of a good instructor May 14, 2002
Verified Purchase
After reading almost all reviews, I actually think I agree with almost all including the ones that say it is not a book for beginners and ones that say that it is a great book written by a very knowledgeable author. As a student who just completed a course in this subject with this book as the text, here is what I would like to say:
1. My instructor re-ordered some of the content of the text for his course. It seemed necessary to understand certain concepts.
2. As one of the previous reviews mentioned, some of the important aspects of probability theory were hidden in problems, these were brought out by the instructor either as homeworks or as part of lecture notes and explained. This also means that it is not enough to just read this text and understand the examples. It is almost as important to go through the problems to get the complete picture
3. All in all I liked the book but I sure would not have liked it as much if I did not have a good instructor to go with it. Definitely not a self-study book.
Comment | 
Was this review helpful to you?
24 of 26 people found the following review helpful
4.0 out of 5 stars great book in the classical textbook sense March 26, 2000
i would like to again point out that while this book is excellent as a reference, it's not very good to read cover-to-cover. Papoulis is extremely knowledgeable in this area, and this book is, in fact, the FIRST EVER book of stochastic/random variables and processes written for the engineers. unfortunately, despite the excellent material, the presentation and coverage is sometimes hard to follow, and hides the true gem in this book.
Comment | 
Was this review helpful to you?
22 of 24 people found the following review helpful
5.0 out of 5 stars Papoulis is Useful July 2, 2002
By A Customer
Format:Hardcover|Verified Purchase
I first encountered the works of Papoulis when just out of graduate school in pure math, and worked for a major defense contractor as an analyst. I found out that almost all the engineers there had this book, and purchased a copy. I had studied stochastic processes at a much more theoretical level than is presented in this book, and that study was significantly more difficult than the material in the text under review, so complainers take note. Why do I think this book an excellent one? Because it is so eminently USEFUL to the working engineer. I believe that has been the intent of the author in all of his works. If you're a working engineer who needs to find answers to tough problems, you can scarcely do better than to consult Papoulis.
For example, the material on power spectra is of more than academic interest and is useful in applications; the bivariate Taylor expansion for moments of a function of two distributions has been used again and again in applications in industry; especially in the analysis of the ratio of noisy variables arising from radar measurements. The point is that the text provides the material in a readily accessible way for someone who needs it in the "real world" of engineering analysis.
Comment | 
Was this review helpful to you?
13 of 15 people found the following review helpful
5.0 out of 5 stars Plenty Of Examples. Great Detail October 12, 2003
This book has a huge pool of examples that enables the reader to understand the concept better. The subject itself is "NOT TRIVIAL", however if it wasn't for this book, it could have been worse. I own this book and I liked it. The examples are fairly easy to understand and relevant to the end of chapter problems. There is also a web site for this book that has a lot of additional resources. So if you are thinking of buying this book, then go for it. (Please Note that I am writing this review for the Fourth Edition Hardcover by Papoulis and Pillai. Previous edition is not that good)
Comment | 
Was this review helpful to you?
12 of 14 people found the following review helpful
5.0 out of 5 stars Not easy but worth the effort February 2, 2004
By A Customer
This is a book which definitely requires diligence and effort to get through. The excercises are also not trivial to say the least. However, if you have the energy and patience to actually slug through this text, in the end you will discover that you have actually learned something. Something which is profound and difficult to understand. This book is definitely not recommended as a casual reference.
Comment | 
Was this review helpful to you?
11 of 13 people found the following review helpful
By A Customer
In very short words this book is just a very long stream of random processes equations with some explanation in between. At the same time, the cross index at the end is not very complete, this makes looking for an answer difficult (try just to put together the most fundamental properties of a Gaussian Process if you doubt about this).
One good feature of this book (and maybe this is why it's so widely used) is that it covers a very extensive list of topics.
Comment | 
Was this review helpful to you?
Most Recent Customer Reviews
5.0 out of 5 stars Classic Book on a Very Difficult Topic
I cut my teeth from the 2nd edition of this classic text and later actually went out and bought the 1st edition (1965)
because multiple people that I work with mentioned that... Read more
Published 4 months ago by sp
3.0 out of 5 stars Material Presented in Clear Albeit Unorganized Fashion
I'm using this book for a a graduate level engineering course on probability theory and random stochastic processes. Read more
Published 4 months ago by Daniel Greenheck
3.0 out of 5 stars Good detailed fundamental basis, but a bit too academic/theoretical...
I ordered this book because someone told me it was a good book about probability. It formalizes the underpinnings and definitions of probablity and random processes, but I find it... Read more
Published 6 months ago by Aero-Mech
5.0 out of 5 stars Great book
It's in a very good condition. Only small differences between the first edition and the latest one. The book itself.......all right, a little bit difficult.
Published 8 months ago by Siyan Lin
4.0 out of 5 stars Expensive, but textbook.
I really need to use it as my textbook so I had to buy it. A good book indeed though.
Published 9 months ago by Mu Yi
5.0 out of 5 stars The Standard
Excellent supplier. Book arrived ahead of time in very good condition.

Of course, this is the standard for anyone interested in developing a basic understanding of the... Read more
Published 12 months ago by Leo Procida
3.0 out of 5 stars The reference in probability.
This book is by no means an easy read, especially as a self-teaching material...

I remember that I found the course I took at university a few decades ago, dense,... Read more
Published 17 months ago by André Gargoura
1.0 out of 5 stars It's not for learning, just for havign a reference of all the...
This book didn't help me to better understand the subject. It just throws formulas and examples with very little explanation of the steps taken to solve them.
Published 17 months ago by Rafael Carvajal Díaz
2.0 out of 5 stars An unfortunate staple
If you are like me, you are required to purchase this book.

Be warned, your the class you are taking will be one of the worst you have ever taken. Read more
Published 17 months ago by Mr. JE
5.0 out of 5 stars Random Variables
This is probably one of the best book written in the subject. It includes most of the material used in digital communication courses
Published 18 months ago by Newton
Search Customer Reviews
Search these reviews only

Sell a Digital Version of This Book in the Kindle Store

If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store. Learn more


There are no discussions about this product yet.
Be the first to discuss this product with the community.
Start a new discussion
First post:
Prompts for sign-in

Look for Similar Items by Category