Classic Problems of Probability (eBook)
336 Seiten
John Wiley & Sons (Verlag)
978-1-118-31431-9 (ISBN)
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.
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.
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
"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)
| Erscheint lt. Verlag | 30.4.2012 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik | |
| Schlagworte | Angewandte Wahrscheinlichkeitsrechnung u. Statistik • Applied Probability & Statistics • Geschichte • Geschichte der Statistik • History • History of Statistics • History Special Topics • Spezialthemen Geschichte • Statistics • Statistik • Wahrscheinlichkeitsrechnung |
| ISBN-10 | 1-118-31431-X / 111831431X |
| ISBN-13 | 978-1-118-31431-9 / 9781118314319 |
| Haben Sie eine Frage zum Produkt? |
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