Weighing the Odds : A Course in Probability and Statistics

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Summary: Vive la difference!
Review: A book that is different, indeed, but this difference is what makes it interesting. It bridges the gap between the teaching of Probability and Statistics, and does so in style. The book IS accessible to students, especially those who are accustomed to learning by thinking and not by rote (alas, an endangered species, during, say, the last forty years of Williams' teaching).

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Summary: Not to be used as a Textbook
Review: If you are looking for a text to learn from, this is NOT the book to choose. Although I do find Williams' to have a good sense of humor, the lack of detailed proofs and examples quickly turns the laughter into frustration. I had to refer to 3 other textbooks and search the internet in order to solve the problems. Certainly, if you have already completed a PhD in Statistics or Mathematics, reading Weighing the Odds may be enjoyable to you. For those who are like me (an MS student with a 4.0), I highly recommend you skip this book & buy "A First Course in Probability" by Sheldon Ross.

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Summary: In common justice
Review: It seems only fair to remark that the invective directed against the book by some Amazon customers is something profoundly different in kind from what one finds in reviews by authoritative people. See, for example, the detailed reviews by Ed Waymire in American Mathematical Monthly, Vol. 110, 2003, pp. 964-967, and by Marjorie Hahn in Computing in Science and Engineering, Vol. 6, 2004, pp. 85-88. In forty years of teaching probability theory, I have had very many students who would not have found a book such as this particularly challenging, but who would have welcomed what challenges it does pose.


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Summary: vintage williams
Review: This is a delightful introduction to probability and mathematical statistics. There are already quite a few nice probability texts at this level (Jim Pitman's PROBABILITY is a favorite of mine) and many serviceable introductions to mathematical statistics (Rice's MATHEMATICAL STATISTICS AND DATA ANALYSIS and Cassella & Berger's STATISTICAL INFERENCE are good examples), but Williams is very different from these. He manages to teach a lot of beautiful probability along with some practical statistics. The approach is thoroughly modern (including in depth coverage of modern Bayesian methods) and reasonably applied (much more applied than you would expect from his other books). He is opinionated, but never boring.

The only negatives I can think of are (1) too few problems, especially easy problems; (2) quite a few typos--it's a first printing; and (3) some asides, especially on measure theoretic issues, that the target audience may find more confusing than helpful.

I wish this book had been around when I first studied this material.

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Summary: Weighing the Odds an absolutely worthless text
Review: This is the worst mathematics book that I have ever used. This book is being used for 2 semesters - Introduction to Probability Theory and Mathematical Statistics. It was completely worthless for the the Introduction to Probability Theory as I had to buy Sheldon Ross' "A First Course in Probability" just to make sense out the course. This book has no examples and the way it is written is often very cryptic. Even the problems that have answers in the back of the book are not explained. Often times the author will just say it is obvious for part of the solution when it is far from obvious. This book needs many more examples and more thorough explanations of topics. This is not the review of a disgruntled student getting a poor grade and just criticizing the text. I am getting an A in the class but no thanks to this worthless text! In fact I plan on burning the book when my course work is finished!