Probability: Theory and Examples (Cambridge Series in Statistical and Probabilistic Mathematics)

The book is very suitable for graduate students major in statistics. The delivery is quick and the book is in good condition. I am satisfied

One of the worst textbooks that I have ever owned. Nothing is clear. Here are some examples."If X and Y are independent and f and g are measurable functions, show that f(X) and g(Y) are independent."Are X and Y random variables, or events? What are the domain of f and g? What measurable?"Find all the joint distributions...(so on, so on.)"Joint distribution is never defined in this book. It is not even in the index.One can most likely figure out by context, but that is not the point. It is a textbook. It must teach us something, and therefore, it has to make every single little thing as clear as it can. I would recommend you to stay away from this textbook, if you are new to the probability theory. If you are required to purchase this book, I would suggest you to have another reference. I think even some of the analysis books do the better job of explaining the probability measure than this one.

I can't believe the amount of rage that the Amazon reviewers have towards this book. Surely there are more deserving books out there. My review will largely be a defense of this book, and I will try to convince potential buyers that this book IS worth their money.First of all, I admit that this isn't a book I would want to first learn from (I did learn from it, so I would know). When I was learning probability theory, I already knew measure theory, and so I wanted a book that would actually use measure theory freely. There are many important theorems, such as the central limit theorem, which demand that the reviewer use measure theory. It is the avoidance of measure theory which makes most elementary books on probability theory uninteresting. On the other hand, most measure-theoretic probability theory books assume that you've learned from an elementary book and so they don't waste time on developing intuition. I've found that most books, Billingsley's included, simply treat probability theory as an extension of measure theory. This is not what I wanted, and I was led to this book.Probability theory is a field with one foot in examples and applications and the other in theory. The thing that this book does better than others, except perhaps for the beautiful, but infinitely long Feller, is that it pays homage to the applications of probability theory. This should be expected, judging from the title. Every page of this book has an example. Every single theorem is used in an interesting example, and there are tons of exercises asking the reader to use the theorems and prove alternative theorems. A student would not leave with a healthy perspective of probability theory if all they learned from were, say, Varadhan's notes or Stroock's analytic book of death. They would know a whole lot of extra measure theory without having any idea of what problems this theory was designed to solve. A student working with Durrett's book will have seen plenty of examples and worked out a huge number of problems themselves. Hence, they will leave this book with a deeper understanding and a more balanced view of probability theory. It is these applications which attracts so many researchers to this book and make them impose it on their students.Now, this book is massive. It sits at a relatively slim 400 pages, but just about all of basic probability theory is in here: sums of independent random variables, basic limit theorems, martingales, markov chains, brownian motion, etc... There is nothing that a student could wish for (except coupling) whichthey won't find in here. As always, trying to learn from massive, sprawling books is a challenge. This expansive coverage makes the book great to have around as a reference and second textbook. There are also tons of tricks that he teaches which are really useful and aren't found easily in other books.Now, there are many complaints about the readability of this book. In the fourth edition, Durrett switched over to LaTeX (as opposed to just TeX I believe) and so the cross references and index have all be corrected. I found the typos in this book to still be too large in number, but they are almost universally trivial. None of the typos confused me. I will blame Durrett for being careless, but not an incompetent expositor. There is one wrong proof somewhere in here that my professor mentioned, so that's unfortunate. Also, when I was first learning probability theory, I found this book difficult to read. However, now that I know a good amount I find this book to be perfectly readable. I suppose it's just best as a second book.Overall, this book does have some flaws (hence, the subtraction of a star), but students will leave with a healthy perspective. This is why this is the best measure-theoretic probability book.

I love it

Very good condition

I am a Ph.D. student in statistics. I REALLY strongly dislike this book.Let me start with a contrast: I studied undergraduate real analysis from Strichartz, and I think that was an excellent book. The proofs were useful for the homework problems, and Strichartz's discussion, while lengthy, was helpful for providing the crucial insights to actually LEARN from the text. While I felt that the textbook was quite difficult for me -- I must have spent about 20 hours a week that semester studying Strichartz -- I felt like I came out of the class with (at least) twice as strong math skills as I did when I entered the course. It is from Strichartz that I learned how to do proofs with quantifiers.However, Durrett's textbook is the kind of textbook which teaches nothing. I do not feel like I could master the material by studying his proofs and "examples." The skills necessary to attack the (challenging) homework problems are not going to be reinforced by this textbook. I learned much more by looking at professor's online solutions to Durrett's problems. And that's what's really missing from this textbook. A good calculus textbook, like the one by James Stewart, is REPLETE with sample problems and fully-worked solutions. Most good calculus teachers know that students learn (inductively) from examples -- it is only LATER that they would care about something like a proof.So what is the point of this textbook? I'm not sure. As far as I'm concerned, it was completely and utterly useless.

The book has lots of writings from a pencil and it is distracting.Has writings on important part of the discussion.Not worth to this amount.

If you are a math PhD and am pretty sure that you are going to make probability as your career, it's a nice book.More precisely, this book is comprehensive in terms of SKILLS that you will need to pass prelims/do research.Though, it is not very good to 'tell the story of probability'. For instance, section 5.4 is called 'Doob’s Inequality, Convergence in Lp'. If you are new to this area, you might wonder why we should study convergence in Lp of martingales. Severe lack of connections between theorems/sections. If you are an undergrad trying to find your interest / grad student in other discipline but want to use some grad probability, for instance, Maybe 'A Probability Path' by Resnick, or 'A First Look at Rigorous Probability' by Rosenthal are better for this purpose.It's a good book, but not for everyone.