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Rating: 
Summary: A Reference in Probability Theory
Review: 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.
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Summary: A "Bible" but ...
Review: I first encountered this book in the summer after my Junior year at Indiana University. It is a two-volume work. The first volume introduces probability from the discrete viewpoint. This volume is filled with interesting applications of the theory and has hundreds of doable, informative and fun problems. Having taught several post-calculus probability courses, I often found myself looking to Feller's volumes for ideas and examples. It is a good introduction for a sophisticated undergraduate to discrete probability. The second volume looks at the measure-theoretic side of the subject. Were I to only own one reference on probability, it would be Feller's book. Feller was a significant player in the probability field in his lifetime and he is also an excellent expositor.
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Summary: Classic intuition book
Review: 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 mathematical tool to prove results. This book's philosophy falls into the second category. 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 the volumes may have known this. I'm not saying which one is more appropriate. But I know that this book is currently the best of all the books 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 you are...
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Summary: daunting, very duanting
Review: This book is one of the tomes of probability theory. The material covered is not for the faint of heart though. The text explains things as do most graduate level math texts, in proofs and theory.
Rating:
Summary: daunting, very duanting
Review: This book is one of the tomes of probability theory. The material covered is not for the faint of heart though. The text explains things as do most graduate level math texts, in proofs and theory.
Rating:
Summary: what is a title?
Review: This is a GREAT book.
Unfortunately, I lost mine.
I wanted to buy volume 1, third edition, to replace the lost book but I got volume 2, second edition. Because volume 1 is SO GREAT book, I decided to keep volume 2 as well. How can be sure I ordered the needed one?
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Summary: great treatment of difficult topics
Review: This is the book we called Feller Volume II in graduate school. We used it to sharpen our intuition about probability. Feller was a master at explaining difficult things in simple ways. This includes the waiting time paradox and Benford's laws. For structure and rigor we looked elsewhere, Chung and/or Neveu. But Feller's books brought a joy and love for the subject. No statistician or probabilist should be without a copy on his shelf!
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Summary: challenging book on probability theory
Review: Will Feller died before I first started reading his work. We used Volume II of these two volumes in my graduate course on probability. My Professor Persi Diaconis used Neveu's calculus of probability for the axiomatic treatment. We also consulted Chung's text. Feller Volume II was used to challenge our intuition and provoke our interest. It did that with the waiting time paradox and Benford's law and many other interesting and difficult things to calculate. Feller explained ideas well taking an intuitive approach rather than a rigorous mathematical one. Feller was one of the great probabilists. He came up with general conditions (Lindeberg-Feller) for the central limit theorem. Volume I deals with the many important discrete probability distributions and the associated combinatorics while Volume II deals with continuous distributions. Both volumes provide interesting and provocative material on probability and it is worthwhile for every statistician and probabilist to have copies on his shelf.
Rating:
Summary: challenging book on probability theory
Review: Will Feller died before I first started reading his work. We used volume II of these two volumes in my graduate course on probability. My Professor Persi Diaconis used Neveu's calculus of probability for the axiomatic treatment. We also consulted Chung's text. Feller Volume II was used to challenge our intuition and provoke our interest. It did that with the waiting time paradox and Benford's law and many other interesting and difficult things to calculate. Feller explained ideas well, taking an intuitive approach rather than a rigorous mathematical one. Feller was one of the great probabilists. He was famous for coming up with general conditions (the Lindeberg-Feller conditions) for the central limit theorem. Volume I deals with the many important discrete probability distributions and the associated combinatorics while Volume II deals with continuous distributions. Both volumes provide interesting and provocative material on probability and it is worthwhile for every statistician and probabilist to have copies on his or her shelf.
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