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基本説明
Provides a clear and concise mathematical treatment and accurate history of classic problems in probability in chronological order.
Full Description
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.
Contents
Preface ix
Acknowledgments xi
1 Cardano and Games of Chance (1564) 1
2 Galileo and a Discovery Concerning Dice (1620) 9
3 The Chevalier de Méré Problem I: The Problem of Dice (1654) 13
4 The Chevalier de Méré Problem II: The Problem of Points (1654) 20
5 Huygens and the Gambler's Ruin (1657) 39
6 The Pepys-Newton Connection (1693) 49
7 Rencontres with Montmort (1708) 54
8 Jacob Bernoulli and his Golden Theorem (1713) 62
9 De Moivre's Problem (1730) 81
10 De Moivre, Gauss, and the Normal Curve (1730, 1809) 89
11 Daniel Bernoulli and the St. Petersburg Problem (1738) 108
12 d'Alembert and the "Croix ou Pile" Article (1754) 119
13 d'Alembert and the Gambler's Fallacy (1761) 124
14 Bayes, Laplace, and Philosophies of Probability (1764, 1774) 129
15 Leibniz's Error (1768) 156
16 The Buffon Needle Problem (1777) 159
17 Bertrand's Ballot Problem (1887) 169
18 Bertrand's Strange Three Boxes (1889) 175
19 Bertrand's Chords (1889) 179
20 Three Coins and a Puzzle from Galton (1894) 186
21 Lewis Carroll's Pillow Problem No. 72 (1894) 189
22 Borel and a Different Kind of Normality (1909) 194
23 Borel's Paradox and Kolmogorov's Axioms (1909, 1933) 199
24 Of Borel, Monkeys, and the New Creationism (1913) 208
25 Kraitchik's Neckties and Newcomb's Problem (1930, 1960) 215
26 Fisher and the Lady Tasting Tea (1935) 224
27 Benford and the Peculiar Behavior of the First Significant Digit (1938) 233
28 Coinciding Birthdays (1939) 240
29 Lévy and the Arc Sine Law (1939) 247
30 Simpson's Paradox (1951) 253
31 Gamow, Stern, and Elevators (1958) 260
32 Monty-Hall, Cars, and Goats (1975) 264
33 Parrondo's Perplexing Paradox (1996) 271
Bibliography 277
Photo Credits 296
Index 299
