Digital Dice: Computational Solutions to Practical Probability Problems

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Princeton University Press, May 4, 2011 - Mathematics - 276 pages
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Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.

Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.

The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.

Digital Dice will appeal to anyone who enjoys popular math or computer science.

 

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Contents

Introduction
1
The Problems
35
MATLAB Solutions To The Problems
101
Appendix 1 One Way to Guess on a Test
221
Appendix 2 An Example of VarianceReduction in the Monte Carlo Method
223
Appendix 3 Random Harmonic Sums
229
Appendix 4 Solving Montmorts Problem by Recursion
231
Appendix 5 An Illustration of the InclusionExclusion Principle
237
Appendix 7 How to Simulate Kelvins Fair Coin with a Biased Coin
248
Appendix 8 How to Simulate an Exponential Random Variable
252
Appendix 9 Index to AuthorCreated MATLAB mFiles in the Book
255
Glossary
257
Acknowledgments
259
Index
261
Also
265
Copyright

Appendix 6 Solutions to the Spin Game
244

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About the author (2011)

Paul J. Nahin is the author of many best-selling popular-math books, including "Chases and Escapes, Dr. Euler's Fabulous Formula, When Least is Best, Duelling Idiots and Other Probability Puzzlers", and "An Imaginary Tale" (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

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