Gorroochurn Classic Problems of Probability

1. Auflage 2012
ISBN: 978-1-118-31431-9
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 336 Seiten, E-Book

Winner of the 2012 PROSE Award for Mathematics from The AmericanPublishers Awards for Professional and Scholarly Excellence.
"A great book, one that I will certainly add to my personallibrary."
--Paul J. Nahin, Professor Emeritus of ElectricalEngineering, University of New Hampshire
Classic Problems of Probability presents a lively accountof the most intriguing aspects of statistics. The book features alarge collection of more than thirty classic probability problemswhich have been carefully selected for their interesting history,the way they have shaped the field, and their counterintuitivenature.
From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713Golden Theorem to Parrondo's 1996 Perplexing Paradox, the bookclearly outlines the puzzles and problems of probability,interweaving the discussion with rich historical detail and thestory of how the mathematicians involved arrived at theirsolutions. Each problem is given an in-depth treatment, includingdetailed and rigorous mathematical proofs as needed. Some of thefascinating topics discussed by the author include:
* Buffon's Needle problem and its ingenious treatment by JosephBarbier, 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 ofprobability
* Coverage of both elementary and more complex problems,including the Chevalier de Méré problems, Fisher and thelady 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 professionalsinterested in the history of probability and the variedproblem-solving strategies employed throughout the ages. The bookalso serves as an insightful supplement for courses on mathematicalprobability and introductory probability and statistics at theundergraduate level.

Autoren/Hrsg.

Gorroochurn, Prakash

Inhaltsverzeichnis

Preface 3
Problem 1. Cardano and Games of Chance (1564) 8
Problem 2. Gailieo and a Discovery Concerning Dice (1620) 15
Problem 3. The Chevalier de Méré Problem I: TheProblem of Dice (1654) 17
Problem 4. The Chevalier de Méré Problem II:The Problem of Points (1654) 22
Problem 5. Huygens and the Gambler's Ruin (1657) 39
Problem 6. The Pepys-Newton Connection (1693) 47
Problem 7. Rencontres with Montmort (1708) 50
Problem 8. Jacob Bernoulli and his Golden Theorem (1713) 54
Problem 9. De Moivre's Problem (1730) 71
Problem 10. De Moivre, Gauss, and the Normal Curve (1730, 1809)79
Problem 11. Daniel Bernoulli and the St Petersburg Problem(1738) 94
Problem 12. D'Alembert and the "Croix ou Pile"Article (1754) 102
Problem 13. D'Alembert and the Gambler's Fallacy(1761) 105
Problem 14. Bayes, Laplace, and Philosophies of Probability(1764, 1774) 109
Problem 15. Leibniz's Error (1768) 132
Problem 16. The Buffon Needle Problem (1777) 134
Problem 17. Bertrand's Ballot Problem (1887) 143
Problem 18. Bertrand's Strange Three Boxes (1889) 147
Problem 19. Bertrand's Chords (1889) 151
Problem 20. Three Coins and a Puzzle from Galton (1894) 156
Problem 21. Lewis Carroll's Pillow Problem No. 72 (1894)157
Problem 22. Borel and A Different Kind of Normality (1909)161
Problem 23. Borel's Paradox and Kolmogorov's Axioms(1909, 1933) 165
Problem 24. Of Borel, Monkeys, and the New Creationism (1913)173
Problem 25. Kraitchik's Neckties and Newcomb'sProblem (1930, 1960)
Problem 26. Fisher and the lady Tasting Tea (1935) 188
Problem 27. Benford and the Peculiar Behavior of the FirstSignificant Digit (1938) 195
Problem 28. Coinciding Birthdays (1939) 200
Problem 29. Lévy and the Arc Sine Law (1939) 206
Problem 30. Simpson's Paradox (1951) 210
Problem 31. Gamow, Stern, and Elevators (1958) 215
Problem 32. Monty-Hall, Cars, and Goats (1975) 218
Problem 33. Parrondo's Perplexing Paradox (1996) 224
Bibliography 230
Photo Credits 254

Über Autor(innen)

PRAKASH GORROOCHURN, PhD, is Assistant Professor in the Department of Biostatistics at Columbia University, where he is also a statistical consultant in the School of Social Work. Dr. Gorroochurn has published extensively in his areas of research interest, which include mathematical population genetics and genetic epidemiology.