Probabilities Problems And Paradoxes

Author : William Eckhardt
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 48,6 Mb
Release : 2012-09-26
Category : Mathematics
ISBN : 9789400751408

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Paradoxes in Probability Theory by William Eckhardt Pdf

Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.​

Author : William Eckhardt
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 53,7 Mb
Release : 2012-09-27
Category : Mathematics
ISBN : 9789400751392

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Paradoxes in Probability Theory by William Eckhardt Pdf

Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.​

Author : Sidney A. Luckenbach
Publisher : Unknown
Page : 310 pages
File Size : 49,5 Mb
Release : 1972
Category : Induction (Logic)
ISBN : OCLC:31478416

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Probabilities, Problems, and Paradoxes by Sidney A. Luckenbach Pdf

Author : Anonim
Publisher : Unknown
Page : 328 pages
File Size : 48,6 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015017297493

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Probabilities, Problems, and Paradoxes by Anonim Pdf

Author : Gábor J. Székely
Publisher : Unknown
Page : 270 pages
File Size : 51,5 Mb
Release : 1986
Category : Mathematical statistics
ISBN : UOM:39015038937226

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Paradoxes in Probability Theory and Mathematical Statistics by Gábor J. Székely Pdf

Author : Anonim
Publisher : Unknown
Page : 326 pages
File Size : 43,5 Mb
Release : 1972
Category : Mathematics
ISBN : MINN:31951D003805935

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Probabilities, Problems, and Paradoxes by Anonim Pdf

Author : Marilyn A. Reba,Douglas R. Shier
Publisher : CRC Press
Page : 605 pages
File Size : 54,9 Mb
Release : 2014-12-15
Category : Mathematics
ISBN : 9781482297935

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Puzzles, Paradoxes, and Problem Solving by Marilyn A. Reba,Douglas R. Shier Pdf

A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress

Author : Gábor J. Székely
Publisher : Springer
Page : 0 pages
File Size : 41,8 Mb
Release : 2001-12-14
Category : Mathematics
ISBN : 9401725330

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Paradoxes in Probability Theory and Mathematical Statistics by Gábor J. Székely Pdf

It isn't that they can't see the solution. Approach your problems from the right end and begin with the answers. It is that they can't see the problem. Then one day, perhaps you will find G. K. Chesterton. The Scandal of the final question. Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowski lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experi mental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Author : John Leslie Mackie
Publisher : Oxford University Press, USA
Page : 322 pages
File Size : 50,7 Mb
Release : 1973
Category : Philosophy
ISBN : 9780198244028

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Truth, Probability and Paradox by John Leslie Mackie Pdf

Classic work by one of the most brilliant figures in post-war analytic philosophy.

Author : Yudi Pawitan,Youngjo Lee
Publisher : CRC Press
Page : 352 pages
File Size : 49,5 Mb
Release : 2024-03-21
Category : Philosophy
ISBN : 9781003849032

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Philosophies, Puzzles and Paradoxes by Yudi Pawitan,Youngjo Lee Pdf

Unlike mathematics, statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, preferences, assumptions and preconceptions of the interpreter, leading to a variety of interpretations of concepts as well as results. Philosophies, Puzzles and Paradoxes: A Statistician’s Search for Truth thoroughly examines the distinct philosophical approaches to statistics – Bayesian, frequentist and likelihood – arising from different interpretations of probability and uncertainty. These differences are highlighted through numerous puzzles and paradoxes and illuminated by extensive discussions of the background philosophy of science. Features: Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinking Discussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist views Exposition and examination of Savage’s axioms as the basis of subjective probability and Bayesian statistics Explanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principle Discussion of fiducial probability and its evolution to confidence procedure Introduction of extended and hierarchical likelihood for random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single events Detailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and more Substantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statistics This book primarily targets statisticians in general, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.

Author : Leonard M. Wapner
Publisher : CRC Press
Page : 222 pages
File Size : 44,8 Mb
Release : 2012-06-04
Category : Mathematics
ISBN : 9781568817217

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Unexpected Expectations by Leonard M. Wapner Pdf

Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on NewBooksinMath.com.

Author : Terence Horgan,Terry Horgan
Publisher : Oxford University Press
Page : 337 pages
File Size : 47,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9780199858422

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Essays on Paradoxes by Terence Horgan,Terry Horgan Pdf

This volume brings together many of Terence Horgan's essays on paradoxes: Newcomb's problem, the Monty Hall problem, the two-envelope paradox, the sorites paradox, and the Sleeping Beauty problem. Newcomb's problem arises because the ordinary concept of practical rationality constitutively includes normative standards that can sometimes come into direct conflict with one another. The Monty Hall problem reveals that sometimes the higher-order fact of one's having reliably received pertinent new first-order information constitutes stronger pertinent new information than does the new first-order information itself. The two-envelope paradox reveals that epistemic-probability contexts are weakly hyper-intensional; that therefore, non-zero epistemic probabilities sometimes accrue to epistemic possibilities that are not metaphysical possibilities; that therefore, the available acts in a given decision problem sometimes can simultaneously possess several different kinds of non-standard expected utility that rank the acts incompatibly. The sorites paradox reveals that a certain kind of logical incoherence is inherent to vagueness, and that therefore, ontological vagueness is impossible. The Sleeping Beauty problem reveals that some questions of probability are properly answered using a generalized variant of standard conditionalization that is applicable to essentially indexical self-locational possibilities, and deploys preliminary probabilities of such possibilities that are not prior probabilities. The volume also includes three new essays: one on Newcomb's problem, one on the Sleeping Beauty problem, and an essay on epistemic probability that articulates and motivates a number of novel claims about epistemic probability that Horgan has come to espouse in the course of his writings on paradoxes. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.

Author : Prakash Gorroochurn
Publisher : John Wiley & Sons
Page : 341 pages
File Size : 43,8 Mb
Release : 2016-05-02
Category : Mathematics
ISBN : 9781118063255

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Classic Problems of Probability by Prakash Gorroochurn Pdf

Winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence. "A great book, one that I will certainly add to my personal library." —Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include: Buffon's Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invariance Various paradoxes raised by Joseph Bertrand Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem The Bayesian paradigm and various philosophies of probability Coverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox Classic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.

Author : Agustin Rayo
Publisher : MIT Press
Page : 321 pages
File Size : 54,7 Mb
Release : 2019-04-02
Category : Mathematics
ISBN : 9780262039413

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On the Brink of Paradox by Agustin Rayo Pdf

An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Author : Leighton Vaughan Williams
Publisher : CRC Press
Page : 311 pages
File Size : 41,9 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781000458879

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Probability, Choice, and Reason by Leighton Vaughan Williams Pdf

Much of our thinking is flawed because it is based on faulty intuition. By using the framework and tools of probability and statistics, we can overcome this to provide solutions to many real-world problems and paradoxes. We show how to do this, and find answers that are frequently very contrary to what we might expect. Along the way, we venture into diverse realms and thought experiments which challenge the way that we see the world. Features: An insightful and engaging discussion of some of the key ideas of probabilistic and statistical thinking Many classic and novel problems, paradoxes, and puzzles An exploration of some of the big questions involving the use of choice and reason in an uncertain world The application of probability, statistics, and Bayesian methods to a wide range of subjects, including economics, finance, law, and medicine Exercises, references, and links for those wishing to cross-reference or to probe further Solutions to exercises at the end of the book This book should serve as an invaluable and fascinating resource for university, college, and high school students who wish to extend their reading, as well as for teachers and lecturers who want to liven up their courses while retaining academic rigour. It will also appeal to anyone who wishes to develop skills with numbers or has an interest in the many statistical and other paradoxes that permeate our lives. Indeed, anyone studying the sciences, social sciences, or humanities on a formal or informal basis will enjoy and benefit from this book.