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Digital Dice:
Computational Solutions to Practical Probability Problems
Paul J. Nahin

Book Description | Reviews
Introduction [in PDF format] | Problems 1 and 2 [HTML] or [PDF format] | Problems 1 and 2 [PDF only] | Solutions 1 [PDF only]

TABLE OF CONTENTS:

Introduction 1

The Problems 35
1. The Clumsy Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve's Elevator Problem 48
7. The Pipe Smoker's Discovery 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandary 61
11. The Case of the Missing Senators 63
12. How Many Runners in a Marathon? 65
13. A Police Patrol Problem 69
14. Parrondo's Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes, and Baby Boys 96

MATLAB Solutions To The Problems 101
1. The Clumsy Dishwasher Problem 103
2. Will Lil and Bill Meet at the Malt Shop? 105
3. A Parallel Parking Question 109
4. A Curious Coin-Flipping Game 114
5. The Gamow-Stern Elevator Puzzle 120
6. Steve's Elevator Problem 124
7. The Pipe Smoker's Discovery 129
8. A Toilet Paper Dilemma 140
9. The Forgetful Burglar Problem 144
10. The Umbrella Quandary 148
11. The Case of the Missing Senators 153
12. How Many Runners in a Marathon? 157
13. A Police Patrol Problem 160
14. Parrondo's Paradox 169
15. How Long is the Wait to Get the Potato Salad? 176
16. The Appeals Court Paradox 184
17. Waiting for Buses 187
18. Waiting for Stoplights 191
19. Electing Emperors and Popes 197
20. An Optimal Stopping Problem 204
21. Chain Reactions, Branching Processes, and Baby Boys 213

Appendix 1. One Way to Guess on a Test 221
Appendix 2. An Example of Variance-Reduction in the Monte Carlo Method 223
Appendix 3. Random Harmonic Sums 229
Appendix 4. Solving Montmort's Problem by Recursion 231
Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237
Appendix 6. Solutions to the Spin Game 244
Appendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin 248
Appendix 8. How to Simulate an Exponential Random Variable 252
Appendix 9. Index to Author-Created MATLAB m-Files in the Book 255

Glossary 257
Acknowledgments 259
Index 261
Also by Paul J. Nahin 264

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File created: 7/11/2014

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