Detailing the history of probability, this book examines the classic problemsof probability, many of which have shaped the field, and emphasizes problems that are counter-intuitive by nature. Classic Problems of Probability is rich in the history of probability while keeping the explanations and discussions as accessible as possible. Each of 33 presented problems contains listing of the latest relevant publications on the topic, and the author provides detailed and rigorous mathematical proofs as needed. For example, in the discussion of the Buffon needle problem, readers will find much more than the conventional discussion found in other books on the topic. The author discusses alternative proofs by Barbier that lead to much more profound and general results. The choice of random variables for which a uniform distribution is possible is also presented, which then naturally leads to a discussion on invariance. Other topics discusses include Cardano, the Chevalier de Mere paradoxes, Jacob Bernoulliand the law of large numbers, the discovery of the normal curve, the lady tasting tea, the Monty-Hall problem, and many more. INDICE: Preface 3Problem 1. Cardano and Games of Chance (1564) 8Problem 2.Gailieo and a Discovery Concerning Dice (1620) 15Problem 3. The Chevalier de Méré Problem I: The Problem of Dice (1654) 17Problem 4. The Chevalier de Méré Problem II: The Problem of Points (1654) 22Problem 5. Huygens and the Gambler’s Ruin (1657) 39Problem 6. The Pepys-Newton Connection (1693) 47Problem 7. Rencontres with Montmort (1708) 50Problem 8. Jacob Bernoulli and his Golden Theorem (1713) 54Problem 9. De Moivre’s Problem (1730) 71Problem 10. De Moivre, Gauss, and the Normal Curve (1730, 1809) 79Problem 11. Daniel Bernoulli and theSt Petersburg Problem (1738) 94Problem 12. D’Alembert and the “Croix ou Pile”Article (1754) 102Problem 13. D’Alembert and the Gambler’s Fallacy (1761) 105Problem 14. Bayes, Laplace, and Philosophies of Probability (1764, 1774) 109Problem 15. Leibniz’s Error (1768) 132Problem 16. The Buffon Needle Problem (1777) 134Problem 17. Bertrand’s Ballot Problem (1887) 143Problem 18. Bertrand’s Strange Three Boxes (1889) 147Problem 19. Bertrand’s Chords (1889) 151Problem 20. Three Coins and a Puzzle from Galton (1894) 156Problem 21. Lewis Carroll’s Pillow Problem No. 72 (1894) 157Problem 22. Borel and A Different Kind of Normality (1909) 161Problem 23. Borel’s Paradox and Kolmogorov’s Axioms (1909, 1933) 165Problem 24. Of Borel, Monkeys, and the New Creationism (1913) 173Problem25. Kraitchik’s Neckties and Newcomb’s Problem (1930, 1960)Problem 26. Fisherand the lady Tasting Tea (1935) 188Problem 27. Benford and the Peculiar Behavior of the First Significant Digit (1938) 195Problem 28. Coinciding Birthdays (1939) 200Problem 29. Lévy and the Arc Sine Law (1939) 206Problem 30. Simpson’s Paradox (1951) 210Problem 31. Gamow, Stern, and Elevators (1958) 215Problem 32. Monty-Hall, Cars, and Goats (1975) 218Problem 33. Parrondo’s Perplexing Paradox (1996) 224Bibliography 230Photo Credits 254
- ISBN: 978-1-118-06325-5
- Editorial: John Wiley & Sons
- Encuadernacion: Rústica
- Páginas: 320
- Fecha Publicación: 29/06/2012
- Nº Volúmenes: 1
- Idioma: Inglés