Digital dice : computational solutions to practical probability problems
Annotation 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 whatDigital Diceis 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 Dicewill appeal to anyone who enjoys popular math or computer science
eBook, English, ©2008
Princeton University Press, Princeton, N.J., ©2008
exercise books
1 online resource (xi, 263 pages) : illustrations
9781400839292, 9781283069595, 9786613069597, 1400839297, 1283069598, 6613069590
730899250
The clumsy dishwasher problem
Will Lil and Bill meet at the malt shop?
A parallel parking question
A curious coin-flipping game
The Gamow-Stern elevator puzzle
Steve's elevator problem
The pipe smoker's discovery
A toilet paper dilemma
The forgetful burglar problem
The umbrella quandary
The case of the missing senators
How many runners in a marathon?
A police patrol problem
Parrondo's paradox
How long is the wait to get the potato salad?
The appeals court paradox
Waiting for buses
Waiting for stoplights
Electing emperors and popes
An optimal stopping problem
Chain reactions, branching processes, and baby boys
Appendixes: 1. One way to guess on a test
2. An example of variance-reduction in the Monte Carlo method
3. Random harmonic sums
4. Solving Montmort's problem by recursion
5. An illustration of the inclusion-exclusion principle
6. Solutions to the spin game
7. How to simulate Kelvin's fair coin with a biased coin
8. How to simulate an exponential random variable
9. Index to author-created MATLAB m-files in the book
English