Counterexamples in Probability And Statistics PDF Download
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Author: Joseph P. Romano
Publisher: CRC Press
ISBN: 9780412989018
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.
Author: Joseph P. Romano
Publisher: CRC Press
ISBN: 9780412989018
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.
Author: Jordan M. Stoyanov
Publisher: Courier Corporation
ISBN: 0486499987
Category : Mathematics
Languages : en
Pages : 404
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Book Description
"While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--
Author: Gary L. Wise
Publisher: Oxford University Press
ISBN: 019536130X
Category : Mathematics
Languages : en
Pages : 224
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Book Description
A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.
Author: Jordan M. Stoyanov
Publisher: Wiley
ISBN: 9780471965381
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Counterexamples (in the mathematical sense) are powerful tools of mathematical theory. This book covers counterexamples from probability theory and stochastic processes. This new expanded edition includes many examples and the latest research results. The author is regarded as one of the foremost experts in the field. Contains numbers examples.
Author: A. A. Sveshnikov
Publisher: Courier Corporation
ISBN: 0486137562
Category : Mathematics
Languages : en
Pages : 516
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Book Description
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.
Author: Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 0486134911
Category : Mathematics
Languages : en
Pages : 226
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Book Description
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Author: Michael A. Proschan
Publisher: CRC Press
ISBN: 1498704204
Category : Mathematics
Languages : en
Pages : 334
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Book Description
Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :
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Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author: Seymour Geisser
Publisher: John Wiley & Sons
ISBN: 0471743127
Category : Mathematics
Languages : en
Pages : 218
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Book Description
A fascinating investigation into the foundations of statistical inference This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses. The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference: * Frequentist * Likelihood * Fiducial * Bayesian The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development. The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.
Author: René L. Schilling
Publisher: Cambridge University Press
ISBN: 1009020390
Category : Mathematics
Languages : en
Pages : 431
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Book Description
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
