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
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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.

An Introduction to the Theory of Probability


Author: Parimal Mukhopadhyay
Publisher: World Scientific
ISBN: 9814313424
Category: Mathematics
Page: 474
View: 1166

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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 Statistical Learning Theory


Author: Sanjeev Kulkarni,Gilbert Harman
Publisher: John Wiley & Sons
ISBN: 9781118023464
Category: Mathematics
Page: 288
View: 3990

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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 Applications of Probability Theory


Author: Henry C. Tuckwell
Publisher: Routledge
ISBN: 1351452959
Category: Mathematics
Page: 308
View: 8193

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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.

An Introduction to Probability Theory


Author: K. Itô
Publisher: Cambridge University Press
ISBN: 9780521269605
Category: Mathematics
Page: 213
View: 7260

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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: John B. Thomas
Publisher: Springer Science & Business Media
ISBN: 1461386586
Category: Mathematics
Page: 250
View: 7285

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This book was written for an introductory one-term course in probability. It is intended to provide the minimum background in probability that is necessary for students interested in applications to engineering and the sciences. Although it is aimed primarily at upperclassmen and beginning graduate students, the only prere quisite is the standard calculus course usually required of under graduates in engineering and science. Most beginning students will have some intuitive notions of the meaning of probability based on experiences involving, for example, games of chance. This book develops from these notions a set of precise and ordered concepts comprising the elementary theory of probability. An attempt has been made to state theorems carefully, but the level of the proofs varies greatly from formal arguments to appeals to intuition. The book is in no way intended as a substi tu te for a rigorous mathematical treatment of probability. How ever, some small amount of the language of formal mathematics is used, so that the student may become better prepared (at least psychologically) either for more formal courses or for study of the literature. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for all of the problems by writing to the author.

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
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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.

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: 2146

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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.

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: 0387955410
Category: Mathematics
Page: 471
View: 6288

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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.

Advanced Statistics from an Elementary Point of View


Author: Michael J. Panik
Publisher: Academic Press
ISBN: 9780120884940
Category: Mathematics
Page: 802
View: 5625

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Advanced Statistics from an Elementary Point of View is a highly readable text that communicates the content of a course in mathematical statistics without imposing too much rigor. It clearly emphasizes the connection between statistics and probability, and helps students concentrate on statistical strategies without being overwhelmed by calculations. The book provides comprehensive coverage of descriptive statistics; detailed treatment of univariate and bivariate probability distributions; and thorough coverage of probability theory with numerous event classifications. This book is designed for statistics majors who are already familiar with introductory calculus and statistics, and can be used in either a one- or two-semester course. It can also serve as a statistics tutorial or review for working professionals. Students who use this book will be well on their way to thinking like a statistician in terms of problem solving and decision-making. Graduates who pursue careers in statistics will continue to find this book useful, due to numerous statistical test procedures (both parametric and non-parametric) and detailed examples. Comprehensive coverage of descriptive statistics More detailed treatment of univariate and bivariate probability distributions Thorough coverage of probability theory with numerous event classifications

The Theory of Probability and the Elements of Statistics


Author: Boris Vladimirovich Gnedenko
Publisher: American Mathematical Soc.
ISBN: 9780821837467
Category: Science
Page: 529
View: 5477

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This classic book is intended to be the first introduction to probability and statistics written with an emphasis on the analytic approach to the problems discussed. Topics include the axiomatic setup of probability theory, polynomial distribution, finite Markov chains, distribution functions and convolution, the laws of large numbers (weak and strong), characteristic functions, the central limit theorem, infinitely divisible distributions, and Markov processes. Written in a clear and concise style, this book by Gnedenko can serve as a textbook for undergraduate and graduate courses in probability.

Elementary applications of probability theory


Author: Henry Clavering Tuckwell
Publisher: CRC Press
ISBN: 9780412304804
Category: Mathematics
Page: 225
View: 2995

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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.

Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions


Author: Aram Aruti?u?novich Sveshnikov,Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 9780486637174
Category: Mathematics
Page: 481
View: 3665

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Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

Elementary Probability Theory


Author: Melvin Hausner
Publisher: Springer Science & Business Media
ISBN: 1461517532
Category: Mathematics
Page: 310
View: 4201

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This text contains ample material for a one term precalculus introduction to probability theory. lt can be used by itself as an elementary introduc tion to probability, or as the probability half of a one-year probability statistics course. Although the development of the subject is rigorous, experimental motivation is maintained throughout the text. Also, statistical and practical applications are given throughout. The core of the text consists of the unstarred sections, most of chapters 1-3 and 5-7. Included are finite probability spaces, com binatorics, set theory, independence and conditional probability, random variables, Chebyshev's theorem, the law of large numbers, the binomial distribution, the normal distribution and the normal approxi mation to the binomial distribution. The starred sections include limiting and infinite processes, a mathematical discussion of symmetry, and game theory. These sections are indicated with an*, and are optional and sometimes more difficult. I have, in most places throughout the text, given decimal equivalents to fractional answers. Thus, while the mathematician finds the answer p = 17/143 satisfactory, the scientist is best appeased by the decimal approximation p = 0.119. A decimal answer gives a ready way of find ing the correct order of magnitude and of comparing probabilities.

Handbook of Probability

Theory and Applications
Author: Tamás Rudas
Publisher: SAGE Publications
ISBN: 1483303659
Category: Social Science
Page: 488
View: 7533

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"This is a valuable reference guide for readers interested in gaining a basic understanding of probability theory or its applications in problem solving in the other disciplines." —CHOICE Providing cutting-edge perspectives and real-world insights into the greater utility of probability and its applications, the Handbook of Probability offers an equal balance of theory and direct applications in a non-technical, yet comprehensive, format. Editor Tamás Rudas and the internationally-known contributors present the material in a manner so that researchers of various backgrounds can use the reference either as a primer for understanding basic probability theory or as a more advanced research tool for specific projects requiring a deeper understanding. The wide-ranging applications of probability presented make it useful for scholars who need to make interdisciplinary connections in their work. Key Features Contains contributions from the international who's-who of probability across several disciplines Offers an equal balance of theory and applications Explains the most important concepts of probability theory in a non-technical yet comprehensive way Provides in-depth examples of recent applications in the social and behavioral sciences as well as education, business, and law Intended Audience This Handbook makes an ideal library purchase. In addition, this volume should also be of interest to individual scholars in the social and behavioral sciences.

Concepts of Probability Theory


Author: Paul E. Pfeiffer
Publisher: Courier Corporation
ISBN: 0486636771
Category: Mathematics
Page: 405
View: 8275

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Using the simple conceptual framework of the Kolmogorov model, this intermediate-level textbook discusses random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. For advanced undergraduate students of science, engineering, or mathematics acquainted with basic calculus. Includes problems with answers and six appendixes. 1965 edition.

An Introduction to Quantum Stochastic Calculus


Author: K.R. Parthasarathy
Publisher: Springer Science & Business Media
ISBN: 3034805667
Category: Mathematics
Page: 290
View: 7468

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An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito’s correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semigroups as well as classical Markov semigroups are realised through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level. - - - This is an excellent volume which will be a valuable companion both to those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students. (Mathematical Reviews) This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field. (Zentralblatt MATH) Elegantly written, with obvious appreciation for fine points of higher mathematics (...) most notable is [the] author's effort to weave classical probability theory into [a] quantum framework. (The American Mathematical Monthly)

The Application of Mathematical Statistics to Chemical Analysis


Author: V. V. Nalimov
Publisher: Elsevier
ISBN: 148318479X
Category: Science
Page: 304
View: 7920

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The Application of Mathematical Statistics to Chemical Analysis presents the methods of mathematical statistics as applied to problems connected with chemical analysis. This book is divided into nine chapters that particularly consider the principal theorems of mathematical statistics that are explained with examples taken from researchers associated with chemical analysis in laboratory work. This text deals first with the problems of mathematical statistics as a means to summarize information in chemical analysis. The next chapters examine the classification of errors, random variables and their characteristics, and the normal distribution in mathematical statistics. These topics are followed by surveys of the application of Poisson's and binomial distribution in radiochemical analysis; the estimation of chemical analytic results; and the principles and application of determination of experimental variance. The last chapters explore the determination of statistical parameters of linear relations and some working methods associated with the statistical design of an experiment. This book will be of great value to analytical chemists and mathematical statisticians.