An Elementary Introduction to the Theory of Probability


Author: Boris Vladimirovich Gnedenko,Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601557
Category: Mathematics
Page: 130
View: 407

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This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

Theory of Probability


Author: Boris V. Gnedenko
Publisher: Routledge
ISBN: 1351408585
Category: Mathematics
Page: 520
View: 8939

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This book is the sixth edition of a classic text that was first published in 1950 in the former Soviet Union. The clear presentation of the subject and extensive applications supported with real data helped establish the book as a standard for the field. To date, it has been published into more that ten languages and has gone through five editions. The sixth edition is a major revision over the fifth. It contains new material and results on the Local Limit Theorem, the Integral Law of Large Numbers, and Characteristic Functions. The new edition retains the feature of developing the subject from intuitive concepts and demonstrating techniques and theory through large numbers of examples. The author has, for the first time, included a brief history of probability and its development. Exercise problems and examples have been revised and new ones added.

An Elementary Introduction to Statistical Learning Theory


Author: Sanjeev Kulkarni,Gilbert Harman
Publisher: John Wiley & Sons
ISBN: 9781118023464
Category: Mathematics
Page: 288
View: 2614

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A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning A joint endeavor from leading researchers in the fields of philosophy and electrical engineering, An Elementary Introduction to Statistical Learning Theory is a comprehensive and accessible primer on the rapidly evolving fields of statistical pattern recognition and statistical learning theory. Explaining these areas at a level and in a way that is not often found in other books on the topic, the authors present the basic theory behind contemporary machine learning and uniquely utilize its foundations as a framework for philosophical thinking about inductive inference. Promoting the fundamental goal of statistical learning, knowing what is achievable and what is not, this book demonstrates the value of a systematic methodology when used along with the needed techniques for evaluating the performance of a learning system. First, an introduction to machine learning is presented that includes brief discussions of applications such as image recognition, speech recognition, medical diagnostics, and statistical arbitrage. To enhance accessibility, two chapters on relevant aspects of probability theory are provided. Subsequent chapters feature coverage of topics such as the pattern recognition problem, optimal Bayes decision rule, the nearest neighbor rule, kernel rules, neural networks, support vector machines, and boosting. Appendices throughout the book explore the relationship between the discussed material and related topics from mathematics, philosophy, psychology, and statistics, drawing insightful connections between problems in these areas and statistical learning theory. All chapters conclude with a summary section, a set of practice questions, and a reference sections that supplies historical notes and additional resources for further study. An Elementary Introduction to Statistical Learning Theory is an excellent book for courses on statistical learning theory, pattern recognition, and machine learning at the upper-undergraduate and graduate levels. It also serves as an introductory reference for researchers and practitioners in the fields of engineering, computer science, philosophy, and cognitive science that would like to further their knowledge of the topic.

Elementary Probability Theory with Stochastic Processes


Author: K. L. Chung
Publisher: Springer Science & Business Media
ISBN: 1475751141
Category: Mathematics
Page: 325
View: 8037

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In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.

An Introduction to the Theory of Point Processes

Volume I: Elementary Theory and Methods
Author: D.J. Daley,D. Vere-Jones
Publisher: Springer Science & Business Media
ISBN: 0387215646
Category: Mathematics
Page: 471
View: 3456

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Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Elementary Probability


Author: David Stirzaker
Publisher: Cambridge University Press
ISBN: 9781139441032
Category: Mathematics
Page: N.A
View: 1950

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Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.

Elementary Applications of Probability Theory, Second Edition


Author: Henry C. Tuckwell
Publisher: CRC Press
ISBN: 9780412576201
Category: Mathematics
Page: 296
View: 2256

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This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.

Foundations of the Theory of Probability

Second English Edition
Author: A.N. Kolmogorov
Publisher: Courier Dover Publications
ISBN: 0486829790
Category: Mathematics
Page: 96
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This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.

Lady Luck

The Theory of Probability
Author: Warren Weaver
Publisher: Courier Corporation
ISBN: 0486150917
Category: Mathematics
Page: 400
View: 1094

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This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.

An Introduction to the Theory of Probability


Author: Parimal Mukhopadhyay
Publisher: World Scientific
ISBN: 9814313424
Category: Mathematics
Page: 474
View: 7748

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The Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution and convergence of random variables. Difficult ideas have been explained lucidly and have been augmented with explanatory notes, examples and exercises. The basic requirement for reading this book is simply a knowledge of mathematics at graduate level. This book tries to explain the difficult ideas in the axiomatic approach to the theory of probability in a clear and comprehensible manner. It includes several unusual distributions including the power series distribution that have been covered in great detail. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging. The author is a former Professor of the Indian Statistical Institute, India.

An Elementary Introduction to Mathematical Finance


Author: Sheldon M. Ross
Publisher: Cambridge University Press
ISBN: 1139498037
Category: Mathematics
Page: N.A
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This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.

The Theory of Probability

Explorations and Applications
Author: Santosh S. Venkatesh
Publisher: Cambridge University Press
ISBN: 1107024471
Category: Mathematics
Page: 805
View: 8346

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From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

An Introduction to Probability Theory


Author: K. Itô
Publisher: Cambridge University Press
ISBN: 9780521269605
Category: Mathematics
Page: 213
View: 2355

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One of the most distinguished probability theorists in the world rigorously explains the basic probabilistic concepts while fostering an intuitive understanding of random phenomena.

Introduction to Probability


Author: Charles Miller Grinstead,James Laurie Snell
Publisher: American Mathematical Soc.
ISBN: 0821894145
Category: Probabilities
Page: 510
View: 5781

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This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. The text is also recommended for use in discrete probability courses. The material is organized so that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization does not emphasize an overly rigorous or formal view of probability and therefore offers some strong pedagogical value. Hence, the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. Features: Key ideas are developed in a somewhat leisurely style, providing a variety of interesting applications to probability and showing some nonintuitive ideas. Over 600 exercises provide the opportunity for practicing skills and developing a sound understanding of ideas. Numerous historical comments deal with the development of discrete probability. The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level. The book contains a lot of examples and an easy development of theory without any sacrifice of rigor, keeping the abstraction to a minimal level. It is indeed a valuable addition to the study of probability theory. --Zentralblatt MATH

Basic Concepts of Probability and Statistics

Second Edition
Author: J. L. Hodges, Jr.,E. L. Lehmann
Publisher: SIAM
ISBN: 9780898719123
Category: Mathematical statistics
Page: 441
View: 4878

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Basic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially in its emphasis on models and model building and also by its coverage of topics such as simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power. The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (Neyman-Pearson) lemma for hypothesis testing. Audience: intended for high school and undergraduate students as well as others who want a mathematically rigorous introduction to probability and statistics that does not require calculus. It can supplement high school and college courses on discrete mathematics and will appeal especially to instructors teaching statistics courses within mathematics departments.

Introduction to the Theory of Random Processes


Author: Iosif Il?ich Gikhman,Anatoli? Vladimirovich Skorokhod
Publisher: Courier Corporation
ISBN: 0486693872
Category: Mathematics
Page: 516
View: 8425

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Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.

The Knot Book

An Elementary Introduction to the Mathematical Theory of Knots
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
ISBN: 0821836781
Category: Mathematics
Page: 306
View: 2645

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Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.

Mathematical Conversations

Multicolor Problems, Problems in the Theory of Numbers, and Random Walks
Author: E. B. Dynkin,V. A. Uspenskii
Publisher: Courier Corporation
ISBN: 0486154912
Category: Mathematics
Page: 288
View: 6309

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Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.