Major changes in this edition include the substitution of probabilistic arguments for combinatorial artifices, and the addition of new sections on branching processes, Markov chains, and the De Moivre-Laplace theorem.
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Most Helpful Customer Reviews
45 of 45 people found the following review helpful:
5.0 out of 5 stars
The grandaddy of all probability books,
By John M. Morrison (Hillsdale, NJ) - See all my reviews
This review is from: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition (Hardcover)
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.
66 of 70 people found the following review helpful:
5.0 out of 5 stars
A Reference in Probability Theory,
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This review is from: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition (Hardcover)
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.
33 of 33 people found the following review helpful:
5.0 out of 5 stars
Felled by Feller?,
By
This review is from: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition (Hardcover)
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
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First Sentence:
The mathematical theory of probability gains practical value and an intuitive meaning in connection with real or conceptual experiments such as tossing a coin once, tossing a coin 100 times, throwing three dice, arranging a deck of cards, matching two decks of cards, playing roulette, observing the life span of a radioactive atom or a person, selecting a random sample of people and observing the number of left-handers in it, crossing two species of plants and observing the phenotypes of the offspring; or with phenomena such as the sex of a newborn baby, the number of busy trunklines in a telephone exchange, the number of calls on a telephone, random noise in an electrical communication system, routine quality control of a production process, frequency of accidents, the number of double stars in a region of the skies, the position of a particle under diffusion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rth return, delayed recurrent events, classical ruin problem, finite mean recurrence times, auxiliary deck, nth trial, arc sine distribution, infinitely rich adversary, unrestricted random walk, rth occurrence, target deck, kth trial, invariant probability distribution, persistent chain, combinatorial product, sample space corresponding, twelve dice, rth success, exponential holding times, summation extending, indistinguishable balls, arc sine law, irreducible chain, discrete sample spaces, pure birth process Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Mathematische Annalen, Journal of Genetics, Physikalische Zeitschrift, Samuel Pepys, Van Nostrand New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The mathematical theory of probability gains practical value and an intuitive meaning in connection with real or conceptual experiments such as tossing a coin once, tossing a coin 100 times, throwing three dice, arranging a deck of cards, matching two decks of cards, playing roulette, observing the life span of a radioactive atom or a person, selecting a random sample of people and observing the number of left-handers in it, crossing two species of plants and observing the phenotypes of the offspring; or with phenomena such as the sex of a newborn baby, the number of busy trunklines in a telephone exchange, the number of calls on a telephone, random noise in an electrical communication system, routine quality control of a production process, frequency of accidents, the number of double stars in a region of the skies, the position of a particle under diffusion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rth return, delayed recurrent events, classical ruin problem, finite mean recurrence times, auxiliary deck, nth trial, arc sine distribution, infinitely rich adversary, unrestricted random walk, rth occurrence, target deck, kth trial, invariant probability distribution, persistent chain, combinatorial product, sample space corresponding, twelve dice, rth success, exponential holding times, summation extending, indistinguishable balls, arc sine law, irreducible chain, discrete sample spaces, pure birth process Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Mathematische Annalen, Journal of Genetics, Physikalische Zeitschrift, Samuel Pepys, Van Nostrand 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 100
books:
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100
books
cite this book:
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- Modern Business Statistics (Wiley series in computers & information processing systems for business) by Ronald L. Iman in Back Matter (1), and Back Matter (2)
- Mathematical Statistics by Steven F. Arnold in Front Matter
- The Statistical Analysis of Failure Time Data (Wiley Series in Probability and Statistics) by John D. Kalbfleisch in Back Matter
- Basic Statistics for Business and Economics (Management & Administration) by Paul G. Hoel in Back Matter
- Continuous Multivariate Distributions (Wiley Series in Probability and Statistics) by S. Kotz in Back Matter
See all 100 books this book cites
- Elements of Applied Stochastic Processes (Wiley Series in Probability and Statistics) by U. Narayan Bhat on 5 pages
- Stochastic Models in Reliability and Maintenance by Shunji Osaki on 4 pages
- Extreme Values in Finance, Telecommunications, and the Environment (Chapman & Hall/CRC Monographs on Statistics & Applied Probability) by Barbel Finkenstadt on page 77, page 281, and page 364
- Boundary Value Problems, Fifth Edition: and Partial Differential Equations by David L. Powers on page 206, and Back Matter
- Exploring Data Tables, Trends, and Shapes by David C. Hoaglin in Front Matter, and page 509
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