Digital Dice: Computational Solutions to Practical Probability ProblemsPrinceton University Press, 24/03/2013 - 288 من الصفحات 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. |
المحتوى
Introduction | 1 |
The Problems | 35 |
The Clumsy Dishwasher Problem | 37 |
Will Lil and Bill Meet at the Malt Shop? | 38 |
A Parallel Parking Question | 40 |
A Curious CoinFlipping Game | 42 |
The GamowStern Elevator Puzzle | 45 |
Steves Elevator Problem | 48 |
The Clumsy Dishwasher Problem | 103 |
Will Lil and Bill Meet at the Malt Shop? | 105 |
A Parallel Parking Question | 109 |
A Curious CoinFlipping Game | 114 |
The GamowStern Elevator Puzzle | 120 |
Steves Elevator Problem | 124 |
The Pipe Smokers Discovery | 129 |
A Toilet Paper Dilemma | 140 |
The Pipe Smokers Discovery | 51 |
A Toilet Paper Dilemma | 53 |
The Forgetful Burglar Problem | 59 |
The Umbrella Quandary | 61 |
The Case of the Missing Senators | 63 |
How Many Runners in a Marathon? | 65 |
Contents 13 A Police Patrol Problem | 69 |
Parrondos Paradox | 74 |
How Long Is the Wait to Get the Potato Salad? | 77 |
The Appeals Court Paradox | 81 |
Waiting for Buses | 83 |
Waiting for Stoplights | 85 |
Electing Emperors and Popes | 87 |
An Optimal Stopping Problem | 91 |
Chain Reactions Branching Processes and Baby Boys | 96 |
MATLAB Solutions To The Problems | 101 |
The Forgetful Burglar Problem | 144 |
The Umbrella Quandary | 148 |
The Case of the Missing Senators | 153 |
How Many Runners in a Marathon? | 157 |
A Police Patrol Problem | 161 |
Parrondos Paradox | 169 |
and Baby Boys | 213 |
One Way to Guess on a Test | 221 |
Random Harmonic Sums | 229 |
An Illustration of the InclusionExclusion | 237 |
Solutions to the Spin Game | 244 |
How to Simulate an Exponential | 252 |
Acknowledgments | 259 |
Also by Paul J Nahin | 265 |