a course in probability theory probability and mathematical statistics 21

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A Course In Probability Theory

Author : Kai Lai Chung
ISBN : 9780080570402
Genre : Mathematics
File Size : 53. 45 MB
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This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

Probability For Statisticians

Author : Galen R. Shorack
ISBN : 9783319522074
Genre : Mathematics
File Size : 52. 34 MB
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The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.

Probability And Mathematical Statistics

Author : Eugene Lukacs
ISBN : 9781483269207
Genre : Mathematics
File Size : 82. 55 MB
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Probability and Mathematical Statistics: An Introduction provides a well-balanced first introduction to probability theory and mathematical statistics. This book is organized into two sections encompassing nine chapters. The first part deals with the concept and elementary properties of probability space, and random variables and their probability distributions. This part also considers the principles of limit theorems, the distribution of random variables, and the so-called student’s distribution. The second part explores pertinent topics in mathematical statistics, including the concept of sampling, estimation, and hypotheses testing. This book is intended primarily for undergraduate statistics students.

Probability Theory

Author : Y. A. Rozanov
ISBN : 9780486321141
Genre : Mathematics
File Size : 44. 18 MB
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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, and more. Includes 150 problems, many with answers.

Problems In Probability Theory Mathematical Statistics And Theory Of Random Functions

Author : A. A. Sveshnikov
ISBN : 9780486137568
Genre : Mathematics
File Size : 37. 30 MB
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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.

A Basic Course In Probability Theory

Author : Rabi Bhattacharya
ISBN : 9783319479743
Genre : Mathematics
File Size : 56. 46 MB
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This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

Probability Theory And Mathematical Statistics For Engineers

Author : V. S. Pugachev
ISBN : 9781483190501
Genre : Mathematics
File Size : 49. 93 MB
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Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education.


Author : John W. Lamperti
ISBN : 9781118150436
Genre : Mathematics
File Size : 36. 61 MB
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The brand new edition of this classic text--with more exercises and easier to use than ever Like the first edition, this new version of Lamperti's classic text succeeds in making this fascinating area of mathematics accessible to readers who have limited knowledge of measure theory and only some familiarity with elementary probability. Streamlined for even greater clarity and with more exercises to help develop and reinforce skills, Probability is ideal for graduate and advanced undergraduate students--both in and out of the classroom. Probability covers: * Probability spaces, random variables, and other fundamental concepts * Laws of large numbers and random series, including the Law of the Iterated Logarithm * Characteristic functions, limiting distributions for sums and maxima, and the "Central Limit Problem" * The Brownian Motion process

An Intermediate Course In Probability

Author : Allan Gut
ISBN : 9781441901620
Genre : Mathematics
File Size : 73. 51 MB
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This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

Introduction To Probability

Author : Charles Miller Grinstead
ISBN : 9780821894149
Genre : Probabilities
File Size : 21. 27 MB
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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

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