An Elementary Introduction to the Theory of Probability

Author: Boris Vladimirovich Gnedenko,Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486601552
Category: Mathematics
Page: 130
View: 1573

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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 Elementary Introduction to Statistical Learning Theory

Author: Sanjeev Kulkarni,Gilbert Harman
Publisher: John Wiley & Sons
ISBN: 9781118023464
Category: Mathematics
Page: 288
View: 3385

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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.

An Introduction to the Theory of Probability

Author: Parimal Mukhopadhyay
Publisher: World Scientific
ISBN: 9814313424
Category: Mathematics
Page: 474
View: 8059

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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.

Elementary Applications of Probability Theory

Author: Henry C. Tuckwell
Publisher: Routledge
ISBN: 1351452959
Category: Mathematics
Page: 308
View: 9510

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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.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung
Publisher: Springer-Verlag
ISBN: 3642670334
Category: Mathematics
Page: 346
View: 4881

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Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1

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: 596

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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.

Handbook of Probability

Theory and Applications
Author: Tamás Rudas
Publisher: SAGE Publications
ISBN: 1483303659
Category: Social Science
Page: 488
View: 4557

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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.

An Introduction to Probability Theory

Author: K. Itô
Publisher: Cambridge University Press
ISBN: 9780521269605
Category: Mathematics
Page: 213
View: 8342

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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.

The Application of Mathematical Statistics to Chemical Analysis

Author: V. V. Nalimov
Publisher: Elsevier
ISBN: 148318479X
Category: Science
Page: 304
View: 8874

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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.

Theory of Markov Processes

Author: E. B. Dynkin
Publisher: Elsevier
ISBN: 1483226107
Category: Mathematics
Page: 220
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Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.

Introduction to Probability and Stochastic Processes with Applications

Author: Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja
Publisher: John Wiley & Sons
ISBN: 1118344960
Category: Mathematics
Page: 614
View: 4571

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An easily accessible, real-world approach to probability andstochastic processes Introduction to Probability and Stochastic Processes withApplications presents a clear, easy-to-understand treatment ofprobability and stochastic processes, providing readers with asolid foundation they can build upon throughout their careers. Withan emphasis on applications in engineering, applied sciences,business and finance, statistics, mathematics, and operationsresearch, the book features numerous real-world examples thatillustrate how random phenomena occur in nature and how to useprobabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basicconcepts of probability to advanced topics for further study,including Itô integrals, martingales, and sigma algebras.Additional topical coverage includes: Distributions of discrete and continuous random variablesfrequently used in applications Random vectors, conditional probability, expectation, andmultivariate normal distributions The laws of large numbers, limit theorems, and convergence ofsequences of random variables Stochastic processes and related applications, particularly inqueueing systems Financial mathematics, including pricing methods such asrisk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisitemathematics and tables of standard distributions for use inapplications are provided, and plentiful exercises, problems, andsolutions are found throughout. Also, a related website featuresadditional exercises with solutions and supplementary material forclassroom use. Introduction to Probability and StochasticProcesses with Applications is an ideal book for probabilitycourses at the upper-undergraduate level. The book is also avaluable reference for researchers and practitioners in the fieldsof engineering, operations research, and computer science whoconduct data analysis to make decisions in their everyday work.

Introduction to Probability

Author: John B. Thomas
Publisher: Springer Science & Business Media
ISBN: 1461386586
Category: Mathematics
Page: 250
View: 8395

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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.

Lectures on the Combinatorics of Free Probability

Author: Alexandru Nica,Roland Speicher
Publisher: Cambridge University Press
ISBN: 0521858526
Page: 417
View: 787

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This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Introduction to Crystallographic Statistics

Author: Uri Shmueli,George Herbert Weiss
Publisher: Oxford University Press
ISBN: 9780198559269
Category: Science
Page: 173
View: 8089

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Modern structural applications of crystallography make extensive use of statistical methods, in particular the probability density function (pdf) of the magnitude of the structure factor. Similarly, direct methods of phase determination have been responsible for much of the success of crystallography - methods based on properties of joint pdfs. This monograph, from two authorities in the field of structure factor statics, presents a survey of techniques and theories in this field of research in a self-contained and consistent way, with an emphasis on the probabilistic principles involved.

Advanced Statistics from an Elementary Point of View

Author: Michael J. Panik
Publisher: Academic Press
ISBN: 9780120884940
Category: Mathematics
Page: 802
View: 1283

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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

An Introduction to the Theory of Point Processes

Volume II: General Theory and Structure
Author: D.J. Daley,David Vere-Jones
Publisher: Springer Science & Business Media
ISBN: 0387213376
Category: Mathematics
Page: 573
View: 3598

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This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

Introduction to Stochastic Models

Author: Roe Goodman
Publisher: Courier Corporation
ISBN: 0486450376
Category: Mathematics
Page: 355
View: 9160

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Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state probabilities, general queuing systems, and renewal processes. Each section features worked examples, and exercises appear at the end of each chapter, with numerical solutions at the back of the book. Suggestions for further reading in stochastic processes, simulation, and various applications also appear at the end.

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.

Quantum Models of Cognition and Decision

Author: Jerome R. Busemeyer,Peter D. Bruza
Publisher: Cambridge University Press
ISBN: 110701199X
Category: Business & Economics
Page: 407
View: 4744

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Introduces principles drawn from quantum theory to present a new framework for modeling human cognition and decision.