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Paradoxes In Probability Theory


Paradoxes In Probability Theory
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Paradoxes In Probability Theory


Paradoxes In Probability Theory
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Author : William Eckhardt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-26

Paradoxes In Probability Theory written by William Eckhardt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-26 with Mathematics categories.


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.​



Paradoxes In Probability Theory


Paradoxes In Probability Theory
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Author : William Eckhardt
language : en
Publisher: Springer
Release Date : 2012-09-27

Paradoxes In Probability Theory written by William Eckhardt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-27 with Mathematics categories.


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.​



Paradoxes In Probability Theory And Mathematical Statistics


Paradoxes In Probability Theory And Mathematical Statistics
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Author : Gábor J. Székely
language : en
Publisher: Springer
Release Date : 1986

Paradoxes In Probability Theory And Mathematical Statistics written by Gábor J. Székely and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.


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.



40 Paradoxes In Logic Probability And Game Theory


40 Paradoxes In Logic Probability And Game Theory
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Author : Presh Talwalkar
language : en
Publisher:
Release Date : 2015-09-21

40 Paradoxes In Logic Probability And Game Theory written by Presh Talwalkar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with categories.


This book contains 40 delightful paradoxes. Here is a small sampling.LOGIC: Is it ever right to ask the question: "May I disturb you?" The very act of asking will disturb the person. And yet, I simply can't know if it's correct to ask the question unless I actually ask the question!PROBABILITY: In 2007, the college football team USC was ranked as 7th in the Harris poll, 6th in the USA Today poll, and 6th in the computer rankings. And yet, when the three polls were averaged, USC ended up as being ranked as the 5th best team overall. How is that possible?GAME THEORY: You play game A that is a losing bet. You also play game B that is a losing bet. Yet when you play games A and B alternately that is a winning bet. How can two losing games combine to make a winning game?



Paradoxes Of Belief And Strategic Rationality


Paradoxes Of Belief And Strategic Rationality
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Author : Robert C. Koons
language : en
Publisher: Cambridge University Press
Release Date : 1992-01-31

Paradoxes Of Belief And Strategic Rationality written by Robert C. Koons and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-31 with Mathematics categories.


The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions.



Paradoxes In Scientific Inference


Paradoxes In Scientific Inference
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Author : Mark Chang
language : en
Publisher: CRC Press
Release Date : 2012-10-15

Paradoxes In Scientific Inference written by Mark Chang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-15 with Computers categories.


Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes.



Voting Paradoxes And How To Deal With Them


Voting Paradoxes And How To Deal With Them
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Author : Hannu Nurmi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Voting Paradoxes And How To Deal With Them written by Hannu Nurmi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Political Science categories.


Voting paradoxes are unpleasant surprises encountered in voting. Typically they suggest that something is wrong with the way in dividual opinions are being expressed or processed in voting. The outcomes are bizarre, unfair or otherwise implausible, given the expressed opinions of voters. Voting paradoxes have an important role in the history of social choice theory. The founding fathers of the theory, Marquis de Condorcet and Jean-Charles de Borda, were keenly aware of some of them. Indeed, much of the work of these and other forerunners of the modern social choice theory dealt with ways of avoiding paradoxes related to voting. One of the early paradoxes, viz. that bearing the name of Condorcet, has subsequently gained such a prominent place in the literature that it is sometimes called the paradox of voting. One of the aims of the present work is to show that Condorcet's is but one of many paradoxes of voting. Some of these are pretty closely interrelated making it meaningful to classify them. This is the second main aim of this book. The third objective is to suggest ways of dealing with paradoxes. Since voting is and has always been an essential instrument of democratic rule, it is of some in terest to find out how voting paradoxes are being dealt with by past and present methods of voting. Of even greater interest is to find ways of minimizing the probability of occurrence of various paradoxes. By their very nature some paradoxes are unavoidable.



Hexaflexagons Probability Paradoxes And The Tower Of Hanoi


Hexaflexagons Probability Paradoxes And The Tower Of Hanoi
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Author : Martin Gardner
language : en
Publisher: Cambridge University Press
Release Date : 2008-09

Hexaflexagons Probability Paradoxes And The Tower Of Hanoi written by Martin Gardner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09 with Mathematics categories.


The first of fifteen updated editions of the collected Mathematical Games of Martin Gardner, king of recreational mathematics.



Probability Choice And Reason


Probability Choice And Reason
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Author : Leighton Vaughan Williams
language : en
Publisher: CRC Press
Release Date : 2021-09-16

Probability Choice And Reason written by Leighton Vaughan Williams and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-16 with Mathematics categories.


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.



Sleight Of Mind


Sleight Of Mind
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Author : Matt Cook
language : en
Publisher: MIT Press
Release Date : 2021-08-03

Sleight Of Mind written by Matt Cook and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-03 with Mathematics categories.


This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.