Customer Reviews (1)

Clear explanation of probability concepts
What I liked about this book is that the author steps through each of the probability concepts slowly and with examples.

He also quizzes you, which helps reinforce the new knowledge. He then tells you what the answer is and explains the reasoning behind the answer.

He explains simple probabilities, combined probabilities, combinations and permutations, and probability by combinations.

This is a great book! I'll be keeping it as a reference. ... Read more

Product Description
Check your work-and your understanding-with this manual, which provides worked-out solutions to the odd-numbered problems in the text. ... Read more

Customer Reviews (9)

Review
The book is very helpful but only had the solutions to the odd problems from the book.

If you're a student. Don't buy it.
If you're a student. Don't buy it. You better ask your TA how to do the questions.
Some of the solutions are confusing. It's expensive and only have half of the answer.

Has answers but lacks explanation.
If you're simply looking to check that your answers are correct, this book does that (for the odd numbered problems, at least). But if you're looking for useful commentary to help you learn the techniques, you won't find that here.

This is by far the most lacking solutions manual I've ever used (I've used more than 20 manuals over the last 5 years). I would caution anyone looking to better learn the material.

Great product!
This is a good solutions manual.Only one suggestion, please include all even problems in it, as well as odd ones.

Thanks

grat condition
delivery date was perfect
condition is really good
it is really helping my homework a lot!! ... Read more

Product Description
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.Amazon.com Review
This text is a classic in probability, statistics, andestimation and in the application of these fields to modern engineeringproblems. Probability, Random Variables, and StochasticProcesses assumes a strong college mathematics background. Thefirst half of the text develops the basic machinery of probability andstatistics from first principles while the second half developsapplications of the basic theory. Topics in the first section includeprobability distributions and densities, random variables and vectors,expectations, covariance, correlations, functions of random variablesand vectors, and conditional distributions and densities. In thisthird edition of the text, the second half of the book has beensubstantially updated and expanded to include new or reviseddiscussions of the following topics: mean square estimation,likelihood tests, maximum entropy methods, Monte Carlo techniques,spectral representations and estimation, sampling theory, bispectraand system identification, cyclostationary processes, deterministicsignals in noise, and the Wiener and Kalman filters. Probability,Random Variables, and Stochastic Processes covers a remarkabledensity of material and the clarity of both presentation and notationmake this book invaluable as a text and a reference. ... Read more

Customer Reviews (32)

Easily the most incomprenesible book written on the subject - EVER
This book should never have made it past an editor.All examples at the theoretical level, nothing is ever explained indepedently. Many cross references, even to chapters that follow the current one.The authors succeed in making relatively simple probability utterly impossible to follow.Rediculous math notations.If your professor uses this text, take another course.

Great book
I have used this book as a course for stochastic processes.This is the prerequisite for every comm. graduate class.Papoulis is an elegant writer and this style suits me well. I prefer the most elegant solution to a problem or proof.I find that this book is excellent for reference and self-teaching.I know that many disagree with me but after all this book is intended for graduate work.There are undergraduate type books that are easier to read but not as insightful.Steve Kay's book is pretty good but lacks the rigor that this book has that makes it difficult to cite as a reference in a publication.As a researcher and professional engineer, I always turn to Papoulis.And though I have many other probability books, I find that Papoulis has better coverage in applications to other fields.The chapter on queuing theory is excellent and was very useful in my networking class.I do believe that this fourth edition is the best in terms of coverage, though the other editions are good also.My only gripe about the fourth edition is the long errata for the 1st printing.Subsequent printings correct much of this but some errors still exist.And now it seem to be only offered on Amazon in softcover.Very unfortunate for this classic.

Not an INTRODUCTION!!!
I cannot believe that this book is used as a classic text book for probability and stochastic processes courses for engineering students.

You definitely shouldn't start learning about probability and random variables with Papoulis.

There are so many Greek symbols in this book that readingit was more like reading Plato's dialogues instead of a math book.

Maybe this book would make sense to someone with an Advanced Math degree or at the graduate level who also can read greek!

changing edition
you are not good becuase you changed my order last time. i ordered forth edition and you sent third edition

Adequate in many ways but falls short of being a classic.
The late Prof. Papoulis received degrees in electrical engineering and mathematics at the National Technical University in Athens and the University of Pennsylvania. This textbook was used in my graduate-level course on 'Probability and Stochastic Processes' as part of my MS in electrical engineering. During the course we managed to cover Chapters 1 - 7 (Probability and Random Variables), and Chapter 15 (Markov Chains). One of the strongest points of this book is the large number of solved examples provided per chapter, as well as end-of-chapter problems for which an electronic solutions manual is available.

WHO SHOULD USE THIS BOOK: From an engineering graduate student's perspective, this textbook is a solid reference tool if you wish to look up the mechanics of individual/joint probability density functions or introductory material on stochastic processes.
However, this book is unsuitable for self-study or for reading from cover-to-cover. Part II of the book which deals with stochastic processes and estimation theory is again somewhat incoherently presented and other textbooks are recommended for an in-depth study of these topics.
... Read more

Customer Reviews (7)

the benchmark
If you could only ever buy one book on probability, this would be the one!

Feller's elegant and lateral approach to the essential elements of probability theory and their application to many diverse and apparently unrelated contexts is head-noddingly inspiring.

Working your way through all the exercises in the book would be an excellent retirment diversion sure to stave off the onset of dementia.

Felled by Feller?
I came across Vol 1 as a maths student in the 1970s.Indeed, the book was suggested to me by a quantum physicist recommended for the Nobel Prize in 1965 (John Ward, now deceased)- Feynman, Schwinger and Tomonaga shared the prize.

This is a difficult book and was not widely used even in the 70s as a textbook.I can recall the word "idiosyncratic" being used by someone to describe the book.The problem is that the book seeks to address deep issues and that requires hard work.It is not the sort of book a struggling student will find helpful.As one matures as a mathematician one can appreciate the incredible depth of the material.As a practical example - about 30 years after I first touched this book a Head of Quant approached me in relation to a paper by Marsaglia on distributions of ratios of normal variates. The verification of Marsgalia's derivation (which is non-trivial) is to be found as a series of 3 problems in Vol 1.

With the development of stochastic calculus in the finance world Feller can look a bit outdated but if you can understand the core material you are doing well.Stochastic calculus would be a push over.

Vols 1 and 2 present a treasure trove for those who want to delve into the area.I still use Feller's coin tossing example from Vol 1 to demonstrate to those in the finance world that their understanding of the "law of averages" is imperfect.

The funny thing is that Vol 2 (which I could never afford as a student) is so hard to get.I think that was because Vol 2 was regarded as even more obscure than Vol 1.I got a copy from Amazon second hand and it is now united with its twin in my study.

Peter Haggstrom
BONDI BEACH AUSTRALIA

An excellent book, but ..
I read some chapters during second year of college, and I found a bit difficult. Later, after college, I read Feller's books (Vol I,II) and I could appreciate Feller's books as excellent : a delicate mix of rigor and intuition that only the verfy gifted can write.

A Reference in Probability Theory
Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory.

Whatever your preferred writing style is, Feller is probably a "must-read" if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture.

Classic intuition book
There are two ways people think about probability. The first is that probablity is a mere branch of measure theory. The second is that it is a discipline in its own right. Measure theory is only used as a mathematicaltool to prove results.

This book's philosophy falls into the secondcategory. William Feller has never thought of it, at least not that I know,as a branch of measure theory. People who have completed both of thevolumes may have known this.

I'm not saying which one is moreappropriate. But I know that this book is currently the best of all thebooks that are based on the second thought... When I need intuitive ideas,I often call for it. I believe you'll find it useful too, no matter who youare... ... Read more

Product Description
PROBABILITY AND MEASURE

Third Edition

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.

Like the previous editions, this new edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory. ... Read more

Customer Reviews (12)

Great as a Reference
The book is a great reference for someone who already knows probability theory but needs to refresh her/his memory. It covers all the basics in measure theory, integration and probability, although it hardly discusses non-probabilistic applications of measure theory (however, in the second edition there is a very nice section on Hausdorff Measure).

The book is not so great as a textbook. Despite covering most of the topics typically included in an introductory course on measure-theoretic probability, the order in which these are presented is far from optimal. There is a lot of repetition and this may confuse a reader who is learning the material for the first time.

Anyone attempting to use this book as a textbook must have some knowledge of elementary (non measure-theoretic) probability and a solid background in multivariable calculus (including epsilon-delta arguments).

Solid and Elementary
This book was my first introduction into probability so I am somewhat sentimentally attached to it. The exposition is very, very careful and there is very little a reader has to do than to read carefully meaning that this text is a solid introduction to a serious probability for upper class undergraduates or beginning graduate students.
As a graduate student I very much appreciated the rigor and detailed approach in this textbook. Some of the topics like independence and martingales are developed with a rigor and details usually missing from undergraduate textbooks. If you do not like books missing any deductions this is your textbook.

But there are problems with the text, the major one being the outline and order of the exposition, sometimes it looks as if it was done at random though even that has been done with intention to facilitate understanding but has somehow gone a bit astray. For example it takes hundreds of pages to get into fairly elementary notions and then they are treated counterintuitive leaving reader without intuitive understanding of the topics. See for example exposition of expectation (general case) that is way too slow after hundreds of pages. Or discrete Markov Chains treatment early enough but completely technical and counterintuitive without ever leading a student to any concrete ideas. The integration topics are sprinkled all over the place as well.

Still I would think this is the text for introductory study of probability only with a instructor furnishing better choice and order of topics than the one presented in the textbook. It surely is one of the most detailed approaches geared toward a serious study. On the level of sofistication it does not come anywhere close to Kallenberg's "Foundations of Modern Probability" or Borovkov's "Probability Theory" but it does provide a treatise with important examples, without omissions (sometimes on the expense of elegance but every time for the benefit of reader), and with a rigor required while still being accessible to a beginning graduate student and thus it provides the important benefits of learning.

This is one of the plausible choices for two semester course in introductory graduate probability with perhaps Kai Lai Chung's classic Stanford textbook as the alternative.

Excellent.... Just beautiful...
First thing, this book isn't not appropriate for undergrads, therefore if you are an undergrad, please look for a suitable book for your level and don't post reviews that may mislead other customers. It is also not appropriate for business majors or fields that deal exclusively with applied statistics and probability.

If you are a graduate student in mathematics, statistics or economics (with concentration in econometrics), if you need theoretical probability, this is a must have book. The proofs are presented in a very solid way. Some are even beautiful masterpieces. The same can be said to some motivation for particular issues,for instance, using diatic expansion to motivate the whole probability theory in the first few sections. There aren't many typos, I personally haven't come across any yet. Shiryaev's Probability book is also very good; however, there are apparently more typos and in my personal opinion the explanations in Billingslley's book are a bit better.

If you think good things come in two's I would suggest you also take a look at a solid, concise and cheap book, Probability Essentials by Jacod and Protter.
Enjoy!!!

An exceptionally good book
I've read portions of almost every measure theoretic probability theory book published. And I've come back to Billingsley. This is a hard book to read through and through if you are a novice; this is not Billingsley's fault - it is just that the subject is hard on first acquaintance.
Billinglsey develops everything from first principles, so if you have the intellectual gumption you ought to be able to read the main text with a knowledge of plain college algebra and a little epsilon-delta practice of the sort that comes from an undergraduate real analysis course. The small print asides are fascinating but they are often addressed to a card carrying mathematician. The November 2003 reviewer who complained that Billingsley uses expectation before defining the integral fails to notice - or at any rate, to point out - that he defines only the expectation of simple random variables in the first chapter, so what is involved is just a sum, not an integral. I could sing my praises on and on. But here is the kernel of this review in a line: this is one of the best books ever written on measure theoretic probability. Full stop.

The book on probability
This book is not for everybody. It is for the professional mathematician (or physicist, or alike). All concepts are very well explained, and Billigsley does go down to the core of everything. It is, as far as I'm concerned, among the best books in math ever written, with favorites such as Feynman's lectures and Herstein's algebra manual. If you are a mathematician and want to have the top reference in probability, this is it. ... Read more

Product Description
This comprehensive introduction to probability and statistics will give you the solid grounding you need no matter what your engineering specialty. Through the use of lively and realistic examples, the author helps you go beyond simply learning about statistics to actually putting the statistical methods to use. Rather than focus on rigorous mathematical development and potentially overwhelming derivations, the book emphasizes concepts, models, methodology, and applications that facilitate your understanding. ... Read more

Customer Reviews (8)

Review
I got the book on time and was very pleased with the condition of the book!

Great Buy and Cheap Too!
It was was a 210 dollar book at my school store and i got it on amazon for about half that price. Nothing better than that, saved some money and still got a book in great condition.

ProbStats Review
Great text but I think it is over priced. I'm not sure why it has to be this expensive. It presents the topics well and gives plenty of examples and problems from real-world situations.

Required Text
The text was required for a first stats course in an applied statistics degree program.The book was much cheaper through Amazon.

The text itself is easy to read and understand. What is aimed at in the course syllabus is covered thoroughly.

Be very cautious
A number of the solutions in the rear of the text are simply wrong.These errors confused several of my students.Given how long this text has been in print, one would expect better editorial work by this point. ... Read more

Product Description

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.

Customer Reviews (25)

too much proof, too little application, hard to read!!!!
I used this book for my statistics class.The author makes simple concept hard to understand.It contains pages of proofs to a simple formula.I tried to follow the proof, but it was confusing.The proofs were not basic and intuitive calculus.It did not help me do well in the class either.I almost forgot what I was trying to prove when I followed through.

The book does not explain how to use the formulas.So, the problem sets are hard, because you are not sure how to apply the formulas.

A lot of the later examples are based on the result of the earlier ones.So, it can be very hard to pick up from the middle of the book.It also happens in the problem set, the result from question 1 is needed to complete question four.

Solid text for the study of probability and statistics for math majors
An earlier edition of this book was the text when I took my first course in probability and statistics. Now that I teach math and computer science at a small college I am always on the lookout for a new text and so I examined this book within that context. The coverage is at a high mathematical level; there are many theorems with proof. However, there are also many worked examples that demonstrate how the theorems are applied. The quality of the exposition is such that it is very readable for those who have gone through a three-semester calculus sequence.
The chapters are:

*) Introduction to probability
*) Conditional probability
*) Random variables and distributions
*) Expectation
*) Special distributions
*) Estimation
*) Sampling distributions of estimators
*) Testing hypotheses
*) Categorical data and nonparamentric methods
*) Linear statistical models
*) Simulation

A large set of problems appears at the end of each chapter and solutions to the odd-numbered ones are included in an appendix.
The high level of readability that I appreciated so much when I learned from an earlier edition has been maintained through this one. I can strongly recommend this book as a text for upper level courses in probability and statistics.

Fantastic Into Probability and Stats Book
This book is a fantastic introduction to probability and statistics.It is clear and presents the material with lots of accompanying intuitive explanations.The book also has lots of great examples that clarify the theory and show how the theory can be applied.This book has a strong focus on Bayesian methods, so it is a good place to start if you are trying to learn Bayesian statistics.I love this book.

The truth about this book.99% of other great reviews are bogus.
This book was not written for students.It was written so that the author can gain respect from his from his academic peers.The explanations are absolutely horrible.It purposely explains simple concepts in overly verbose, complicated ways.The idea is to make the subject appear as complicated as possible when it doesn't need to be.It reads like those academic papers that are purposely written in overly complicated language so that nobody understands what the author is talking about except the author himself.The idea is to impress his academic circle by showing that he did a "complicated" analysis.

When are these people going to learn that "simplicity is the ultimate sophistication" - Da Vinci?

Here's an example.Do you know what's a percentile?Think about your SAT or GRE score report.80th percentile means 80% of the people scored lower than you.90th percentile means 90% of the people scored lower than you.Simple, right?This book introduces the concept like this:

"The d.f. of a random variable X gives us the probability that X<=x for all real numbers x.It is often the case that we choose a probability, like 1/2, and we want to know where in the distribution of X we can find that probability.For example, suppose that X is the amount of rain that will fall tomorrow and we want to place an even-money bet on X as follows.If X<=x0, we win one dollar and if X>x0 we lose one dollar.In order to make this bet fair, we need Pr(X<=xo)=Pr(X>x0)=1/2.We could use all the real numbers x trying to find one such that F(x)=1/2, and then we could let x0 equal the value we found.If F is a one-to-one function, then F has an inverse F^-1 and x0=F^-1(1/2)." - P.114

Lol! If you want to learn like this, go ahead and buy this book.I'll give this book two stars because there are probably a few souls out there who actually do prefer to learn like this.

Best intro reference for graduate students
This is by far the best graduate text for basic probability and statistics that is currently made.It even nicely incorporates Bayesian material in a completely relevant way.No, it is probably too complex and abstract for complete beginners in probability as many of the reviewers here have suggested.For anyone with even just a basic background in statistics or probability, however, it is perfect.It is straightforward, comprehensive and most importantly highly readable.There is no comparison to other probability/statistics texts I own--if you are pursuing any sort of graduate level study in statistics or basic probability this the textbook to own and reference. ... Read more

Product Description
The 2006 INFORMS Expository Writing Award-winning and best-selling author Sheldon Ross (University of Southern California) teams up with Erol Peköz (Boston University) to bring you this textbook for undergraduate and graduate students in statistics, mathematics, engineering, finance, and actuarial science.This is a guided tour designed to give familiarity with advanced topics in probability without having to wade through the exhaustive coverage of the classic advanced probability theory books.Topics include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion. No other text covers all these advanced topics rigorously but at such an accessible level;all you need is calculus and material from a first undergraduate course in probability. ... Read more

Customer Reviews (1)

Elegant and Concise
It is difficult to overstate just how exceptional and unique this book is. It is a beautifully precise rendering of the essentials of measure-theoretic probability that conveys the essence of the subjects underlying principles with clarity and economy, coupled with always interesting examples. ... Read more

Product Description
Fully worked solutions to odd-numbered exercises ... Read more

Customer Reviews (29)

Great book for beginning
This book is great if you have no knowledge about Statistics and Probability. It clearly explains ideas and after every new theorem it includes many solved examples. The only thing i am unhappy with this book is it doesn't have solutions of end of chapter exercises but you can still buy solution's manual if you want.

stat book solutions manual
this comment refers to the previous edition of the walpole textbook solutions manual, not the most recent edition (2007?). it has been helpful. especially when the problems require the combination of 2 different probability distributions. most problems i've been assigned have been straightforward. but when you're stuck, and it's an odd problem, seeing how it's done can be very helpful.

No errata???
I'm floored that I'm shelling out $100 for this textbook and the publisher make *no* errata available for download.I've been using this textbook for all of a week, and I've already found two mistakes in chapter 2 alone.Chapter 2 is stuff I already *know*.What am I supposed to do for material I'm learning?

Helpful
This book does a pretty good job of explaining the problems and how they got the answer. I would definitely recommend it.

Terrible
This book manages to efficiently and masterfully destroy any shred of interest and enthusiasm that a student may have for the subject of mathematical probability and statistics. I took a probability and statistics class where the teacher was in no way useful to me. As such, I was forced to rely on this book. I quickly gave up on attempting to obtain even a marginal understanding of the subject and resorted to blindly memorizing formulas and theorems in the hopes that I could deceive the grader into thinking that I was actually competent with the material. I ended up doing well in the class, but despised every moment spent working towards that goal. This book would probably be useful as a reference for somebody already familiar with the subject, or looking to brush up on the material. However, I cannot, in good faith, recommend this book to anybody attempting to learn this subject. ... Read more

Customer Reviews (5)

Student Solutions Manual, somewhat helpful
This solutions manual has some errors in it and some of the worked out problems do not match the problems in the book. Not sure that it was reviewed fully. The solutions are somewhat hard to follow and not complete for some problems. I think it is a great addition to helping me learn Probability and Statistics but I was hoping for a better manual since there is not an instructor's manual available yet.

not a good solution manual
The solution is very brief, which makes it hard to follow.I have this solution manual. I know should rate like everyone else and give it 5 star so can sell my copy.But, I think your money is worth more than that.

So, I give it 2 star.
1. There are too few steps to the final answer.It's almost like the back of the book.
2. The steps shown in the manual is not enough to understand how to solve the problem.
3. The manual only solves odd number problems.If you stuck on an even number, good luck!

I don't want to discourage anyone from buying this, but if you are trying to use this solution manual, and have a self-study, chances are, you get more confused than what you try to understand.You need someone to explain the intermediate steps that's not in the book.

Solid and Helpful
My biggest problem with this solutions manual is that it only solves the odd problems, not the even problems. (For that, I guess you'd have to talk to a professor if you're taking a class, or find the answers somewhere else.) Even with that, it's still a handy item to have around when working on problem sets in the book (Probability and Statistics). I highly suggest this item if you have any problem with the course material.

great
has everything you would expect.answers to half the problems in the book worked out.i didnt give it 5 stars because it would have been nice to have all the answers but i knew what i was buying before hand so its no problem.

wrong title
They gave me the wrong title. I thought I was getting the actual book. It didn't say anywhere that it was only the student solutions manual. ... Read more

Product Description
This book covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. Written by a Fellow of the Casualty Actuarial Society and the Society of Actuaries with many years of experience as a university professor and industry practitioner, the book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering as well as a reference for practitioners in these fields. The book is particularly well suited for students preparing for professional exams, and for several years it has been recommended as a textbook on the syllabus of examinations for the Casualty Actuarial Society and the Society of Actuaries. In addition to covering the standard topics and probability distributions, this book includes separate sections on more specialized topics such as mixtures and compound distributions, distributions of transformations, and the application of specialized distributions such as the Pareto, beta, and Weibull. The book also has a number of unique features such as a detailed description of the celebrated Markowitz investment portfolio selection model. A separate section contains information on how graphs of the specific distributions studied in the book can be created using MathematicaTM. The book includes a large number of problems of varying difficulty. A student manual with solutions to selected problems is available. For more information regarding the student manual, please contact AMS Member and Customer Services at cust-serv@ams.org. An instructor's manual with complete solutions to all the problems as well as supplementary material is available to teachers using the book as the text for the class. To receive it, send e-mail to textbooks@ams.org. ... Read more

Customer Reviews (7)

4.5 stars-The correct title is Probability:The Science of Risk
The author has ,unfortunately,incorrectly categorized the subject matter that he is dealing with in his book.The book deals with known probability distributions that are continuous or discrete.One can calculate the mean,variance,and standard deviation .This means that one is dealing with risk,not uncertainty .The author correctly emphasizes that all the information(sample space of all possible outcomes) must be knownfor each probability distribution to be applied in advance of any decision.

The author discusses Keynes's principle of indifference under the heading equal likelihoods/principle of nonsufficient reason.He overlooks the major thrust of Keynes's position ,which was that ,especially in the fields of social science,liberal arts,economics,finance,business,education,behavioral science,and everyday practical decision making,the decision maker does NOT have the complete information set necessary to specify a particular probability distribution.This problem is generally dealt with by actuaries under the title " credibilities ".

THe book does a good job of illustrating the application of mathematical probability in cases where the laws of addition and multiplication can be applied .Applications of decision trees ,tree diagrams,combinations ,permutations,probability distributions,etc.,are presented effectively.

I recommend the book for individuals who are interested in mathematical probability and the concept of mathematical risk.

Good for self-study
I used this textbook as my main study material for the SOA/CAS P/1 exam. I found it to be well-written and understandable. I have some background in calculus and probability (long-forgotten college courses). I'm hanging on to it for future reference. It's actually possible to learn the material from the book all on your own. All in all, one of the better textbooks out there.

I use this book almost every day
I appreciate that many people will be buying this because it has been endorsed by the Society of Actuaries. My review is for those who aren't being compelled to use the book in exam prep. I find "The Science of Uncertainty" to be the most consistently useful of the statistics texts in my office. The examples are clear, it has the right equations, and it's well organized.

Some people here are complaining of inaccuracies but they provide no examples and, frankly, I've never noticed a problem.

I like that authors provided an appendix explaining how to manipulate the distributions they discuss in the book using Mathematica. This was not new to me, but I can imagine it would save others some headaches.

Excellent for SOA exam P
I used this book to study for SOA exam P and loved it! If you already have some background in statistics and probability, this is the book to go. It will fill in the blanks left by your average school textbook and give you the nesessary coverage of the exam material.

A hard book to digest
As a statistics graduate, I found it hard to understand this book. There are not many friendly examples to help the readers to understand the concepts, even with the help of solution manual. There are some mistakes too. ... Read more

Product Description

This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.

From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

Customer Reviews (5)

Probability
Did not recieve the item in two days when I paid extra for expedited shipping.Recieved it 3 weeks later

A very good book indeed
A reviewer who has given this book 2 stars below says "It was the only math textbook that I really struggled with". That tells me this guy shouldn't have been in a maths course in the first place; stick to drama or English dude, they may be a little taxing for your brain. There should be a rule on Amazon against letting idiots review books of substance.

Chung's book is rich in historical notes, motivation and intuitive development of the subject. Chung is a world-renowned probabilst and also is a gifted writer. This book was followed in my undergraduate days and I still have fond memories of it.

My only gripe is that the new edition has added stuff by another author on finance. There was no need for this whatsoever.

best textbook for elementary probability theory
As a professor in computer science, I am teaching a seminar course in which I wanted to cover basic probability theory in a week.I read at least a half dozen textbooks in the university library and found this book to be far better than others for my purpose.In particular, the material I used was the derivation from the binomial distribution (a coin toss) to the normal and the Poisson distributions, which I covered in two classes.Students liked the many interesting, real-life examples in the book. In addition, I taught the two proofs for the law of large numbers.The second one from Chebyshev was more powerful (applies to non-identical distributions), stronger (guaratees the speed of convergence), simpler and shorter (half a page with no need of mathematical analysis).It eclipsed the theories of other mathematicians in the previous 200 years.The Chebyshev's theorem was new to me and to all the people I mentioned this to.

Of the books I know, this is the best entry level textbook for probability theories.I did not read the chapters on mathematical finance.

Great thoughts in every page
I just read the review by another reader, I would say unfortunately he was wrong. This book is one of the greatest probability book I have ever seen. If you want high-school level combination problem, this book is not for you. But if you want the essence of probability theory, this will be the perfect book for the entry. Actually I'm annoied by the comments of the other reviewer. I think he needs to review himself if he is not competent enough to take such course.

painful... even by undergraduate math textbook standards
I remember this ghastly nightmare from my undergraduate days. It was the only math textbook that I really struggled with. Part of that was probably due to having an inordinately lousy professor, but part of it is because the book reads more like a quick review for people who already know the subject matter than as an actual tool for learning.

As a contrast, check out what people are saying about "A Book of Abstract Algebra" by Pinter -- they're right, THAT is everything a math textbook should be. My class never quite finished it, but I had no trouble reading the later chapters on my own. I still have a copy of Chung's book, but it only has one remotely interesting thing in it that I remember, which was Laplace's calculation of the probability that the sun will rise tomorrow.

Bottom line: if you're unfortunate enough to end up with a professor who is still using Chung's book (I used it in 1997) ... run! ... Read more

Product Description
A self-study guide for practicing engineers, scientists, and students, this book offers practical, worked-out examples on continuous and discrete probability for problem-solving courses. It is filled with handy diagrams, examples, and solutions that greatly aid in the comprehension of a variety of probability problems. ... Read more

Customer Reviews (3)

highly useful book on basic probability with calculus
A friend of mine had Carol Ash as his professor for probability theory back in the late '80s and he remembers her quite fondly.Upon looking through the book he told me this a write-up of her lecture notes.Taking probability (a notoriously difficult subject) around the same time I didn't get so lucky.The professor was decent but the book was not and I struggled with probability topics (though curiously enough, I still have it and use it as a reference--time cures all wounds :).

Much later I taught probability and statistics and drew a lot of examples, problems, and explanations for class from this book.It's quite good and very well written, worth your time if you need some extra help understanding your textbook (many of these are shockingly bad) or for self-study.One big selling point is that the problems are quite thoroughly worked out with intermediate steps explained.

Helped Me Learn a Difficult Subject
Like a good tutor,the "Probability Tutoring Book"explained and clarified points that I'd learned from my instructor and textbook in introductory Probability. Ash's explanations are often very helpful, and her book is loaded with good practice problems.The section on Combinatorics is probably a little too difficult, but I finally managed to grasp the concepts by consulting and doing problems from an old, very helpful book from the library: "Probability: A First Course" by Mosteller, Rourke, and Thomas.Overall, I give Ash's "Probability Tutoring Book" a very high rating as an aid to mastering the fundamentals of probability theory.

Thank God for Dr. Ash
This is a truly terrific book covering the basics of probability theory, but it goes far beyond a mere topical treatment of the subject.I was preparing to take a graduate course required for getting a PhD instatistics, and this book was an excellent way to get a leg up in thecourse.It is clear to me that a great deal of effort and thought was putinto making this an excellent text.Thank you Dr. Ash! ... Read more

Product Description
Students with some previous exposure to Fourier optics or linear theory will find the material particularly absorbing and easy to understand. Contains many new applications to optical and physical phenomena. Softcover. ... Read more

Customer Reviews (1)

Good probability and statistics book
I purchased this book as a reference and tool book "AFTER" I took the class 2 years ago.
Generally it's a book for probability and statistics and it's the textbook in U Arizona Optics ... Read more

Product Description
Concise advanced-level introduction to stochastic processes that frequently arise in applied probability. Largely self-contained text covers Poisson process, renewal theory, Markov chains, inventory theory, Brownian motion and continuous time optimization models, much more. Problems and references at chapter ends. "excellent introduction."—Jrnl. of the American Statistical Association. Bibliography. 1970 edition.
... Read more

Customer Reviews (2)

Good introductory book
I am disappointed a little because I needed more details on this subject.
However, this is great introductory book on the topic.
Will be great for someone who studies 'probability and optimization' or 'Stochastic optimization', for the first time.

Muy interesante
Libro realmente interesante, que aporta un nuevo enfoque ... Read more

Product Description
The purpose of "The Pleasures of Probability" is to introduce some of the most fundamental ideas in classical probability to a fairly general audience - reaching from mathematical amateurs to scientists, from students to professional mathematicians. The only prerequisites required are a decent background in elementary algebra and an interest in discussions of a variety of problems and applications in probability. The style is informal, and the chapters are more like essays on a particular topic than textbook treatments. Even well-known problems are often covered in more depth than usual in order to illustrate underlying ideas. The book can be used as a text for a first course in probability or as a companion to a text. Each chapter ends with a few problems, the answers to which are given at the end of the book. ... Read more

Customer Reviews (3)

nice intro to probability
Professor Isaac has written a book for those interested in learning about probability. It is at a high school algebra level although knowledge of calculus could be helpful at times. He starts with the now famous Monte Hall problem and provides the most lucid explanation I have seen to date. This is a great way to introduce important probability notions such as sample space and probability models for the sample outcomes. Deals mainly with discrete probability which is easiest to understand and yet rich with applications in gambling and other areas.
Important theory is presented but without the detailed mathematical proofs. Covers the gambler's ruin, geometric probability, Monte Carlo methods and some statistical decision theory. He also presents both the frequentist (throughout the text)and the Bayesian paradigms (Chapter 4) for statistical inference. Examples of the application of probability to statistical inference is nicely treated in Chapter 15. The deeper material on Markov chains and Brownian motion are relegated to the last two chapters (16 and 17). The exposition is excellent throughout and many good references are provided for readers who want to learn more or delve deeper into the theory.

very good book - fun for amateurs
This is a wonderful book for both the serious and amateur mathematician. For the serious student and practitioner it will provide an excellent background. For the amateur who enjoy dabbling and reading about math, this is a wonderful book - just read the opening section which explains clearly and an illustrated fashion the Monty Hall problem.

Excellent introduction
This introduction to probability and statistics teaches you about important concepts, theorems and applications without going into proving most of them. It's easily accessible to amateur mathematicians with a bitof persistance, and it illuminates many of its concepts using famousproblems. I'm going to take a statistics course next year, and I found thisto be a delightful introduction to the topic. ... Read more

Product Description

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Customer Reviews (7)

Great book but kindle edition totally flawed
Great book but kindle edition totally flawed. The format does not support mathematical notations, or the conversion from PDF or whatever, is a mess. I also have the Liggett on Interacting particles systems, and it does not have this problem, as far as I know. As a result, formulas look like puzzles with the pieces in disorder. Sometimes, the first line of the statement comes second, and the second comes first (easy puzzle, I agree). Affects almost every theorem in the chapter on ergodic theory and stationary processes, for instance, and, very likely, all over the book. It is really a case of suing Amazon or whoever is responsible ... The format (epub ?)does not like the notation for "equal in distribution", with a letter d on top of a sign "equal" : very often the sign equal is missing. I should have my money back, though I am able to guess the correct version most of the time... But, very likely, a beginner will have a hard time. A pirate PDF version would be better on my iPad, but I did not find any (actually I did not look for one) ...

good treatment of probability theory
When I was a graduate student at Stanford I took a seminar on point processes taught by Ross Leadbetter who was visiting Stanford for the summer. We used Kallenberg's book "Random Measures". That book provided a concise and mathematically rigorous treatment of random measures. This text on probability is a much larger volume but is masterfully presented.
Kallenberg in his usual rigorous style presents the basic measure theory in the first two chapters. He then covers most of the standard probability theory in the next three chapters. Random variables and processes are covered in chapter 3 with the concepts of convergence and independents and the important zero-one laws. Probability distributions, expectations and higher order moments are also covered in chapter 3.

Chapter 4 deals with random sequences and series and averages and includes the strong law of large numbers and Kolmogorov's three series theorem. Chapter 5 covers characteristic functions and important limit theorems including the central limit theorem (Lindeberg-Feller version).

Conditioning and coupling are covered in Chapter 6 and martingales, submartingales and optional stopping are also covered. Upcrossing inequalities and maxima are also discussed here.

Stochastic processes are covered in chapters 8 - 10 and point processes in chapters 11 and 12. Chapter 13 introduces Gaussian processes and Brownian motion. The law of the iterated logarithm is presented in chapter 13 also. Chapter 14 deals with the important Skorohod embedding technique and invariance principles.

The remaining 13 chapters cover many advanced ideas including convergence of random processes and measures, stochastic integrals and Ito calculus, Feller processes and semi-groups, ergodic theory for Markov processes, stochastic differential equations, diffusions, semi-martingales, large deviations, connections with partial differential equations and more.

This book contains every topic I have seen in texts on advanced probability and more! Kallenberg tends to be both rigorous and elegant in his presentation.

This book is for graduate student and probabilists and mathematical statisticians who need these tools to establish limit theorems. It is not intended for an undergraduate course in probability for non-mathematicians. It requires an understanding of advanced mathematics.

Quite hard to add anything more
... to all the comments of the readers below and to the editorial reviews of Kallenberg's book.

One thing I would like to stress is that the proofs in the book can be trusted. This cannot be said for all books on Probability, especially because the subject has been used and abused a lot.

Incredible book, almost self-contained!
This book has accomplished something few people will consider feasible.It covers numerous important topics in 600 pages which ordinarily will be available only in several books andmonographs combined together with total number of pages easily exceeding 2000!Nevertheless, the author has done it not by cheating or handwaving as found in some other books - like those familiar words "this topic is beyond the scope of the present book " or "the proof is omitted for lack of space" etc.As far as I have read, the book is in principle self contained.I venture to bet that a reader comfortable with rigorous calculus and rudimentary topology can already attempt tackling it.

But this is not to say that the book is easy.The first two chapters already constitute a reasonable exposition of measure theory and Lebesgue integration, in only 44 pages.The first ten chapters in 200 pages will suffice for a usual graduate course in probability.To accomplish this feat the author has obviously done a lot of soul searching which manifests itself in almost every page.In the author's own words: "I had to be extremely selective in the choice of material...it was necessary to look for the most economical approach to every result I did decide to include... I was surprised to see how much could actually be done to simplify and streamline proofs, often handed down through generations of textbook writers...Over the years I have developed a personal approach to almost every topic, and even experts might find something of interest. "And indeed he has successfully isolated the bare essences of proofs without being unreasonably terse or leaving the reader disorientated - the few misprints and rarely undefined symbols will not be a serious problem for the active reader, although a passive spectator will have a hard time to get through the book's dense forest.Kallenberg's fine balance between brevity and readability will be a delight for mature mathematicians and provide an enormously fruitful exercise for the students.

All in all, Kallenberg has accomplish an amazing survey of probability theory up to the seventies.What about the more recent results?In his 2001 preface, he says that "probability theory keeps growing at an ever increasing rate, and I am painfully aware that I will never catch up in my efforts to survey the entire subject... a comprehensive treatment of the more recent developments would require another volume or two.I am asking for the reader's patience and understanding." The very idea of a comprehensive treatment of contemporary probability in a single volume or two seems quixotic - if it comes from any other person.But Kallenberg has already performed a Mission Impossible.Maybe he will astound us twice in the future!

The BEST book on modern probability
a) Well organized!
b) Covers a broad range of topics e.g. measure theory, stochastic processes, martingales, Markov processes, stochastic calculus, SDE...and much more!! You can find in it almost all branches of probability!
c) Proofs are short, efficient and interesting, but you have to fill in many details. This gives you a good training!!
d) Results are usually stated in the most general form
e) It requires a strong backgroung in real analysis and functional analysis
e) Very very few typos! ... Read more

Product Description
Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.

While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.
... Read more

Customer Reviews (4)

Probability for pure mathematicians
This book assumes that you have a certain degree of mathematical maturity, but gives you very thorough proofs of the basic concepts of rigorous probability. There is no hand waving here. You are expected to have followed an introduction to measure theory. Don't expect to go through this book in a term, but when you have finished it you will be able to consider yourself to be able to come up with proofs like a mathematician. In other words it will leave you with solid foundations.
I can not imagine this book being used as an introduction.
When you are finished you should be ready for a book like Foundations of Modern Probability.

good graduate probability text
This text by Chung was one of the texts that I used when I was taking a graduate course in probability at Stanford in 1975. It is carefully written but challenging. It provides good coverage of the central limit theorem, the law of large numbers and the law of the iterated logarithm. It also covers stable laws very well. The style is one of rigorous mathematics with theorems, and lemmas given with their mathematical proofs.
The book was recently revised. The revised text does not change much but new material on measure and integration that is now commonly included in the first graduate course in probability has been added. In the 1970s at Stanford a course in measure theory was a prerequisite for the course in advanced probability although some student took it concurrently.

If you plan to get this text, the revised edition is probably worth it. If you already have this edition and know your measure theory, it may not be worth it to get the new edition.

A well organized textbook
There are several nice books in Grad-level Probability Theory. Billingsley's "Probability and Measure" is the richest one, but somehow poor organized and unpleasant printing. Resnick's "Probability Path" serve best for those who has no time to prepare first in measure theory and Lebesque integration but sacrifice some detail in latter part of the book. If you don't have previous Real Analysis training, I would suggest read Resnick first, and then find Billingsley for reference. But if you already good at measure and integration, Kai Lai Chung's "A Course in Probability Theory" still the best textbook teach step by step without losing detail. Chung's style is friendly to self studying like Resnick, but cover more detail in latter part of the book than Resnick. Chung's book is the best companion fot typical one semester course regradless what textbook your teacher choose. In the other words , Resnick helps students significantly in first half of the semester, Chung helps in the whole semester, and Billingsley may offer best effort after you took the Probability Theory course.

the best buy
"A course in probability theory", written by Kai Lai Chung, has been referred by not only mathematicians but also mathematical economists.This book is written very rigorously, but almost all of the theorems have easy-to-understand proofs. So it is not difficult to follow.Moreover, there are lots of exercises in this book. So I do recommend this book. ... Read more

Product Description
Learn the tools to assess product reliability! Haldar and Mahadevan crystallize the research and experience of the last few decades into the most up-to-date book on risk-based design concepts in engineering available. The fundamentals of reliability and statistics necessary for risk-based engineering analysis and design are clearly presented. And with the help of many practical examples integrated throughout the text, the material is made very relevant to today's practice. Key Features
* Covers all the fundamental concepts and mathematical skills needed to conduct reliability assessments.
* Presents the most widely-used reliability assessment methods.
* Concepts that are required for the implementation of risk-based design in practical problems are developed gradually.
* Both risk-based and deterministic design concepts are included to show the transition from traditional to modern design practice. ... Read more

Customer Reviews (4)

Student of Dr. Mahadevan
Excellent text with an abundance of practical examples which demonstrate and apply the material of the text. Very interesting and concise.

Probability,Reliability,and Statiscal Methods in Engineering Design
This book was ordered per the request from Professor at University of California, San Diego - Structural Engineering Department

Simply superb !
As a reliability engineer, I do a lot of probabilistic risk analysis and reliability based design for large systems like gas turbines, etc. From both a theoretical and applied perspective, this is an excellent text for those getting into this subject.

The book is written in a pleasing style, in which complex ideas are introduced in a manner than anyone (with no prior statistical training) can understand. It is a small book that packs a lot of information in it, and the companion volume by the same authors is another excellent text on the same topic. I particularly liked their treatment of LRFD methods and the FORM algorithms.

On the negative side, I found the algorithms described in Madsen's "Methods of structural safety" easier to implement. The authors might want to incorporate some of those methods in their next edition. They could also discuss approaches to model time-dependent reliability, apart from including empirical probability distributions in design.

Overall, I have read most of the texts out there in reliability-based design and this is clearly the best. It's an expensive book, but well worth the money !

This book is One of the Best
This book is among one of the best books in this subject.It captures all different aspects of probability, reliability and statistical methods in engineering design in one book with clear details and examples.The latestadvancements in this area are also included in this book.I do recommendit for any engineering student taking courses in this area. ... Read more

Product Description
The fourth edition of "Probability, Random Variables and Random Signal Principles" continues the success of previous editions with its concise introduction to probability theory for the junior-senior level course in electrical engineering. The book offers a careful, logical organization which stresses fundamentals and includes almost 900 student exercises and abundant practical applications for engineers to understand probability concepts.

The most important new material in this edition relates to discrete-time random processes and sequences, and other topics in the general area of digital signal processing, such as the DT linear system. ... Read more

Customer Reviews (8)

One of most confusing books I had to deal with
Unfortunately I had to get the book in order to follow with the rest of the class.
This book isn't terrible but with out instructor's well contribution this will get you confused and lost on many places.

Great on review; terrible in introducing the target subject matter
This book is simply "okay."It is formatted nicely and easy to look at.The first few chapters on the review of statistics is generally nice (and even led me to question the negative reviews from others until I progressed further).

Mid-way through Chapter 6, just about when stationarity is introduced, the text becomes useless to anyone who is not familiar with the subject matter.Intuition is none-existent in the topics presented - to the extent that I was confused by the presentation of subjects that I was already strong with.

I am told Gardner's book is an excellent book with deep intuition; I have ordered it and will read it with the possibility of returning to peebles after I have a much better idea of what's going on.

Horrible book
The book offers no rigor in any sense and the author seems to have simply copied a large number of formulas from a real probability book. Explanations are sparse and incoherent with vague references to "important applications" with no sense of the abstract concept and virtually no insight into any of the information presented; as another reviewer wrote it is quite dry, I can't see Ben Stein narrating it, but I can picture the author sitting at his keyboard haphazardly plunking in text from other 'sources' all the while wondering what it means.

Skip this and get something with more substance, Peebles offers nothing more than you could find on wikipedia, perhaps less.

A bad book to start with..
This book though looks simple and pretends to present concepts in a lucid manner, does not match international standards. Very few examples are present with less/no illustrations. I struggled with this book for almost 2 years to understand the concepts as this book was the only popular book in my UG college and was readily available in our library. It has ideally no practical examples which can easily discourage reader. After reading contemporary books from Prof Roy Yates and Prof Leon-Garcia, I could do little favor for this book by giving 1 star.

However, one who is already thorough with concepts can use this book for revision. There is a huge element of risk involved in starting with this book to learn probability concepts.

Very little examples, no answers in the back of the book
This book does not have enough examples in the text.I tend to learn better by example and this book is not for people like myself.Also, there are no solutions to any of the homework problems in the back of the book.So you can't check your answers to see if you are doing the problems right. ... Read more