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Probability Theory: A Concise Course [Paperback]

Y. A. Rozanov
4.3 out of 5 stars  See all reviews (3 customer reviews)
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Book Description

June 1 1977 0486635449 978-0486635446 New edition
This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, a detailed treatment of Markov chains, continuous Markov processes, and more. Includes 150 problems, many with answers. Indispensable to mathematicians and natural scientists alike.

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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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4.3 out of 5 stars
4.3 out of 5 stars
Most helpful customer reviews
Format:Paperback
It is amazing that a 148 page book can cover so much with such clarity. Even more amazing is the way it covers all basics, going from combinatorial problems to limit theorems in the first half, with a measure of relevant examples and a good selection of problems. It makes an equally excellent choice of "additional topics": Markov chains and processes, information theory, game theory, branching processes, and optimal control.
This book is not for everyone, as it does require a small degree of mathematical sophistication. But it will prove most useful for a very large audience. For serious beginning mathematics and science students it will provide the quickest way to learn the subject. For lecturers devising an introductory probability course it will make an excellent textbook. And, most importantly, for mathematicians and scientists of all kinds it will serve as an indispensable concise reference book.
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3.0 out of 5 stars not a good first book on probability June 12 2000
Format:Paperback
The problem with this book is that there is no way you can understand the later chapters based on the earlier chapters. This is a more like the survey of the important topics in probability and stochastic processes. There are appendices on information theory, game theory, and branching processes. The book includes basic concepts of probability, random variables, and Markov chains. Feller has a better introductory book on probability.
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5.0 out of 5 stars Excellent Pocket Reference Aug. 21 2002
Format:Paperback
This is not meant as an introductory text--rather, it's a very handy reference for major concepts needed in probability and stochastic calculus. It was one of the few places where I could find a proof of the DeMoivre-Laplace theorem.
The examples are also very good--they touch upon basic problems in the field without being overly trivial.
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.5 out of 5 stars  15 reviews
42 of 42 people found the following review helpful
5.0 out of 5 stars The best introductory probablity book for a serious reader Aug. 22 2003
By Dr. Hoenikker - Published on Amazon.com
Format:Paperback
It is amazing that a 148 page book can cover so much with such clarity. Even more amazing is the way it covers all basics, going from combinatorial problems to limit theorems in the first half, with a measure of relevant examples and a good selection of problems. It makes an equally excellent choice of "additional topics": Markov chains and processes, information theory, game theory, branching processes, and optimal control.
This book is not for everyone, as it does require a small degree of mathematical sophistication. But it will prove most useful for a very large audience. For serious beginning mathematics and science students it will provide the quickest way to learn the subject. For lecturers devising an introductory probability course it will make an excellent textbook. And, most importantly, for mathematicians and scientists of all kinds it will serve as an indispensable concise reference book.
21 of 23 people found the following review helpful
5.0 out of 5 stars Excellent Pocket Reference Aug. 21 2002
By Norman Kabir - Published on Amazon.com
Format:Paperback
This is not meant as an introductory text--rather, it's a very handy reference for major concepts needed in probability and stochastic calculus. It was one of the few places where I could find a proof of the DeMoivre-Laplace theorem.
The examples are also very good--they touch upon basic problems in the field without being overly trivial.
11 of 13 people found the following review helpful
5.0 out of 5 stars fundamentals of probability Aug. 21 2008
By Palle E T Jorgensen - Published on Amazon.com
Format:Paperback
There are quite a number of books offering a quick introduction to the fundamentals of probability. And there is a demand, as these tools have many practical uses: Testing data, sampling, insurance topics, quality checking, finance, investment, and finance, to mention only a few. Rozanov's book, of just a little over 100 pages, helps the novice turning practical problems into numbers. What it does well is letting the beginning student acquire a sense of what the rules are, events, combination of events using the mathematical notions of union and intersection; show how they yield computations with probability, distributions; dependence and independence, repeated experiments; and use of conditional probability. It concludes with limit theorems, Markov chains and Markov processes.
There are other nice books that go beyond Rozanov; for example Heathcote's PROBABILITY, also in the Dover series.
Review by Palle Jorgensen, August 2008.
6 of 6 people found the following review helpful
5.0 out of 5 stars nice, inexpensive and very informative Oct. 26 2005
By Gilles Benson - Published on Amazon.com
Format:Paperback
This a really nice book to begin probability with; then it opens up to deeper parts of the theory, especially branching process and Markov chains within its very thin format; it obviously cannot compete with Feller's monumental work which is a natural follow-up to this one but you can't tackle with Feller from scratch either...So, have look at this one and then try Feller (and avoid getting lost in it...)
5 of 5 people found the following review helpful
5.0 out of 5 stars Excellent for What It Is Nov. 6 2012
By Jason Dowd - Published on Amazon.com
Format:Paperback|Verified Purchase
"Concise" is indeed the operative word here. This book is probably not suitable as a first text on the subject, but makes an excellent review or quick reference for the topics it covers.

Essentially, this text is geared toward taking someone who has - in principle - no knowledge of probability and introducing them specifically to Markov processes. There is very little attention paid to conditional probabilities, and Bayes' rule is never even mentioned.

Also, this book requires no measure theory.

Chapter 1 covers basic concepts: probability as relative frequency, sampling with and without replacement, binomial and multinomial coefficients.

Chapter 2 is titled "Combination of Events". It introduces the idea of the sample space, and focuses on how probability interacts with set theoretic operations such as intersection and union. It ends with a proof of the First Borel-Cantelli Lemma.

The third chapter introduces independence and ends with a proof of the Second Borel-Cantelli Lemma.

The Borel-Cantelli Lemmas are somewhat technical results that are needed to the get the theory of Markov processes off the ground, so it's pretty clear where this book is headed early on. The proofs of both of the lemmas are very tidy.

Chapter 4 is devoted to random variables. Here we find the definitions of expectation, variance, and the correlation coefficient along with Chebyshev's Inequality.

Chapter 5 covers the Bernoulli distribution, the Poisson distribution, and the Normal distribution. We are also treated to the De Moivre-Laplace theorem as a stepping stone toward the Central Limit Theorem.

Chapter 6 is titled "Some Limit Theorems". We are immediately provided with the proof and then statement - in that order - of the Weak Law of Large Numbers. We are then provided merely with the statement of the Strong Law of Large Numbers. This chapter then introduces Generating Functions which are used quite heavily in the remainder of the work. This chapter also introduces Characteristic Functions, which don't get much attention and concludes with the Central Limit Theorem.

Chapter 7 introduces Markov Chains while chapter 8 covers Continuous Markov Processes and naturally covers the Chapman-Kolmogorov equations. Here simply called the Kolmogorov equations for the fairly obvious reason that the author is Russian.

The book ends with four short appendices which introduce the reader in turn to the following topics: Information Theory, Game Theory, Branching Processes, and Optimal Control. I thought these were wonderful although obviously none of them covers very much ground.

This book is actually quite delightful especially for someone who already has some background in basic probability. It does provide and good and very quick introduction to Markov processes, but it's scope of coverage of any topic is necessarily quite limited.
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