This book offers a straightforward introduction to the mathematical theory of probability. It presents the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.
Probability (Springer Texts in Statistics)
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Most Helpful Customer Reviews
5.0 out of 5 stars
Excellent reference,
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This review is from: Probability (Springer Texts in Statistics) (Hardcover)
This is my preferred introduction to probability theory. It is a clearly written and pleasant to read reference.
3.0 out of 5 stars
Pretty average,
This review is from: Probability (Springer Texts in Statistics) (Hardcover)
This is a passable book on probability. It is a halfway house between undergraduate probability and measure theoretic probability. Generally speaking, it lacks rigour; statements like "the proof is surprisingly difficult so we only give a heuristic justification" are not good enough, especially when the author does not then bother to refer the reader to a source where the proof can be found. Also, I felt that not enough was done to frame things in the language of measure theory.
Overall, the exposition is serviceable but dull. There are also a lot of typographical errors (missed out words and typos in equations) and a few incorrect proofs (e.g. the proof of Minkowski's inequality). All in all, considering its flaws and price, you can "probably" do a lot better.
3.0 out of 5 stars
A decent graduate text on probability,
By Clueless "YC" (NJ United States) - See all my reviews
This review is from: Probability (Springer Texts in Statistics) (Hardcover)
This is the text book we used when I took a probability course in Johns Hopkins. The book covers all basic topics and provides a fair introduction to measure-theory based probability theory (without heavy dose of measure theory). However, when it gets to more advanced topics, like the chapters on the central limit theorems and martingales, the text is less lucid and full of typos and mistakes. At times, it became so frustrating to read that I could only wish we had used a better book.
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Inside This Book
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First Sentence:
Probability is the mathematics of uncertainty. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
disjoint blocks theorem, submartingale with respect, monotone continuity, pointwise inverse, simple random variables, optional sampling theorems, monotone class theorem, technical asides, observable random variables, monotone convergence theorem, second term converges, integrable random variables, sure convergence, martingale convergence theorem, uniform integrability, countable partition, positive random variables, standard normal density function, iterated logarithm, other random variables, continuity points, countable additivity Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Probability is the mathematics of uncertainty. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
disjoint blocks theorem, submartingale with respect, monotone continuity, pointwise inverse, simple random variables, optional sampling theorems, monotone class theorem, technical asides, observable random variables, monotone convergence theorem, second term converges, integrable random variables, sure convergence, martingale convergence theorem, uniform integrability, countable partition, positive random variables, standard normal density function, iterated logarithm, other random variables, continuity points, countable additivity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Technical Aside New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 28
books:
See all 28 books this book cites
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Front Matter, and Back Matter
- Real and Complex Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin in Back Matter
- Probability and Measure, 3rd Edition by Patrick Billingsley in Back Matter
- Mathematical Statistics: Basic Ideas and Selected Topics, Vol I (2nd Edition) by Peter J. Bickel in Back Matter
- Probability: Theory and Examples (Probability: Theory & Examples) by Richard Durrett in Back Matter
See all 28 books this book cites
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