Description
Book SynopsisProviding insight into one of the most fascinating and unique subjects in statistics, this book examines classic problems of probability that have both contributed to the field and have been of historical significance, including Parrondo's Amazing Paradox, Laplace's Rule of Succession, and Jacob Bernoulli and His Golden Theorem.
Trade Review“Thus, the book can be highly recommend to every lecturer in this field and every student interested in probability and statistics.” (Zentralblatt Math, 1 September 2013)
Table of ContentsPreface 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
