Digital dice computational solutions to practical probability problems

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....

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Hlavný autor:	Nahin, Paul J
Médium:	E-kniha Kniha
Jazyk:	English
Vydavateľské údaje:	Princeton Princeton University Press 2013
Vydanie:	1
Edícia:	Princeton Puzzlers
Predmet:	Addition Algorithm Algorithms Almost surely Ballot Bus Calculation College of Cardinals Computer programming Computer scientist COMPUTERS / Mathematical & Statistical Software Conviction Customer Data processing Deliberation Desk Dishwasher Elaboration Error Estimation Expected value Exponential distribution Fair coin Floor and ceiling functions Flowchart Geometric probability Histogram Imperial election Inclusion–exclusion principle Integer Location (geography) Mathematician MATHEMATICS MATHEMATICS / Probability & Statistics / General MATHEMATICS / Recreations & Games MathWorks MATLAB Medicine man Monte Carlo method Nuclear fission product Nuclear weapon Percentage Petitioner Police car Polynomial Probabilities Probability Probability density function Probability theory Problem statement Problems, exercises, etc Pure mathematics Quantity Random number Random number generation Random permutation Random variable Result Sample Size Sample space Sampling (statistics) Server (computing) Simulation Sorting algorithm Special case Stanislaw Ulam Statistics Stochastic process Subroutine Summation Technology Textbook Traffic light Umbrella Uranium-235 Variable (computer science) Variance reduction Voting While loop Polynomial Histogram Exponential distribution Floor and ceiling functions Customer Stanislaw Ulam MathWorks Inclusion–exclusion principle Stochastic process MATLAB Result Sorting algorithm Sampling (statistics) Variable (computer science) Probability density function Umbrella Conviction Desk Calculation Location (geography) Random variable Fair coin Monte Carlo method Addition Estimation Dishwasher Almost surely Algorithm Deliberation Expected value Sample Size Random permutation Geometric probability Problem statement Textbook Special case Summation Subroutine Mathematics Random number Nuclear weapon Imperial election Voting Pure mathematics Computer scientist Medicine man Petitioner While loop Sample space Random number generation Elaboration Bus Computer programming Uranium-235 Percentage Probability theory Probability College of Cardinals Quantity Error Police car Mathematician Flowchart Ballot Nuclear fission product Integer Simulation Variance reduction Traffic light Server (computing)
ISBN:	9780691126982, 0691158215, 0691126984, 9780691158211, 9781400846115, 1400846110
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Digital dice: computational solutions to (practical probability problems -- Contents -- Introduction -- The Problems -- 1. The Clumsy Dishwasher Problem -- 2. Will Lil and Bill Meet at the Malt Shop? -- 3. A Parallel Parking Question -- 4. A Curious Coin-Flipping Game -- 5. The Gamow-Stern Elevator Puzzle -- 6. Steve's Elevator Problem -- 7. The Pipe Smoker's Discovery -- 8. A Toilet Paper Dilemma -- 9. The Forgetful Burglar Problem -- 10. The Umbrella Quandary -- 11. The Case of the Missing Senators -- 12. How Many Runners in a Marathon? -- 13. A Police Patrol Problem -- 14. Parrondo's Paradox -- 15. How Long Is the Wait to Get the Potato Salad? -- 16. The Appeals Court Paradox -- 17. Waiting for Buses -- 18. Waiting for Stoplights -- 19. Electing Emperors and Popes -- 20. An Optimal Stopping Problem -- 21. Chain Reactions, Branching Processes, and Baby Boys -- The Solutions -- 1. The Clumsy Dishwasher Problem -- 2. Will Lil and Bill Meet at the Malt Shop? -- 3. A Parallel Parking Question -- 4. A Curious Coin-Flipping Game -- 5. The Gamow-Stern Elevator Puzzle -- 6. Steve's Elevator Problem -- 7. The Pipe Smoker's Discovery -- 8. A Toilet Paper Dilemma -- 9. The Forgetful Burglar Problem -- 10. The Umbrella Quandary -- 11. The Case of the Missing Senators -- 12. How Many Runners in a Marathon? -- 13. A Police Patrol Problem -- 14. Parrondo's Paradox -- 15. How Long is the Wait to Get the Potato Salad? -- 16. The Appeals Court Paradox -- 17. Waiting for Buses -- 18. Waiting for Stoplights -- 19. Electing Emperors and Popes -- 20. An Optimal Stopping Problem -- 21. Chain Reactions, Branching Processes, and Baby Boys -- Appendix 1: One Way to Guess on a Test -- Appendix 2: An Example of Variance-Reduction in the Monte Carlo Method -- Appendix 3: Random Harmonic Sums -- Appendix 4: Solving Montmort's Problem by Recursion -- Appendix 5: An Illustration of the Inclusion-Exclusion Principle -- Appendix 6: Solutions to the Spin Game -- Appendix 7: How to Simulate Kelvin's Fair Coin with a Biased Coin -- Appendix 8: How to Simulate an Exponential Random Variable -- Appendix 9: Index to Author-Created MATLAB m-Files in the Book -- Glossary -- Acknowledgments -- Index.
Front Matter Table of Contents Preface to the Paperback Edition Introduction 1.: The Clumsy Dishwasher Problem 2.: Will Lil and Bill Meet at the Malt Shop? 3.: A Parallel Parking Question 4.: A Curious Coin-Flipping Game 5.: The Gamow-Stern Elevator Puzzle 6.: Steve’s Elevator Problem 7.: The Pipe Smoker’s Discovery 8.: A Toilet Paper Dilemma 9.: The Forgetful Burglar Problem 10.: The Umbrella Quandary 11.: The Case of the Missing Senators 12.: How Many Runners in a Marathon? 13.: A Police Patrol Problem 14.: Parrondo’s Paradox 15.: How Long Is the Wait to Get the Potato Salad? 16.: The Appeals Court Paradox 17.: Waiting for Buses 18.: Waiting for Stoplights 19.: Electing Emperors and Popes 20.: An Optimal Stopping Problem 21.: Chain Reactions, Branching Processes, and Baby Boys 1.: The Clumsy Dishwasher Problem 2.: Will Lil and Bill Meet at the Malt Shop? 3.: A Parallel Parking Question 4.: A Curious Coin-Flipping Game 5.: The Gamow-Stern Elevator Puzzle 6.: Steve’s Elevator Problem 7.: The Pipe Smoker’s Discovery 8.: A Toilet Paper Dilemma 9.: The Forgetful Burglar Problem 10.: The Umbrella Quandary 11.: The Case of the Missing Senators 12.: How Many Runners in a Marathon? 13.: A Police Patrol Problem 14.: Parrondo’s Paradox 15.: How Long Is the Wait to Get the Potato Salad? 16.: The Appeals Court Paradox 17.: Waiting for Buses 18.: Waiting for Stoplights 19.: Electing Emperors and Popes 20.: An Optimal Stopping Problem 21.: Chain Reactions, Branching Processes, and Baby Boys Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Appendix 8 Appendix 9 Glossary Acknowledgments Index Also by Paul J. Nahin
Cover -- Title -- Copyright -- Dedication -- Comments on Probability and Monte Carlo -- Contents -- Preface to the Paperback Edition -- Introduction -- The Problems -- 1. The Clumsy Dishwasher Problem -- 2. Will Lil and Bill Meet at the Malt Shop? -- 3. A Parallel Parking Question -- 4. A Curious Coin-Flipping Game -- 5. The Gamow-Stern Elevator Puzzle -- 6. Steve's Elevator Problem -- 7. The Pipe Smoker's Discovery -- 8. A Toilet Paper Dilemma -- 9. The Forgetful Burglar Problem -- 10. The Umbrella Quandary -- 11. The Case of the Missing Senators -- 12. How Many Runners in a Marathon? -- 13. A Police Patrol Problem -- 14. Parrondo's Paradox -- 15. How Long Is the Wait to Get the Potato Salad? -- 16. The Appeals Court Paradox -- 17. Waiting for Buses -- 18. Waiting for Stoplights -- 19. Electing Emperors and Popes -- 20. An Optimal Stopping Problem -- 21. Chain Reactions, Branching Processes, and Baby Boys -- MATLAB Solutions To The Problems -- 1. The Clumsy Dishwasher Problem -- 2. Will Lil and Bill Meet at the Malt Shop? -- 3. A Parallel Parking Question -- 4. A Curious Coin-Flipping Game -- 5. The Gamow-Stern Elevator Puzzle -- 6. Steve's Elevator Problem -- 7. The Pipe Smoker's Discovery -- 8. A Toilet Paper Dilemma -- 9. The Forgetful Burglar Problem -- 10. The Umbrella Quandary -- 11. The Case of the Missing Senators -- 12. How Many Runners in a Marathon? -- 13. A Police Patrol Problem -- 14. Parrondo's Paradox -- 15. How Long is the Wait to Get the Potato Salad? -- 16. The Appeals Court Paradox -- 17. Waiting for Buses -- 18. Waiting for Stoplights -- 19. Electing Emperors and Popes -- 20. An Optimal Stopping Problem -- 21. Chain Reactions, Branching Processes, and Baby Boys -- Appendix 1. One Way to Guess on a Test -- Appendix 2. An Example of Variance-Reduction in the Monte Carlo Method -- Appendix 3. Random Harmonic Sums
Appendix 4. Solving Montmort's Problem by Recursion -- Appendix 5. An Illustration of the Inclusion-Exclusion Principle -- Appendix 6. Solutions to the Spin Game -- Appendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin -- Appendix 8. How to Simulate an Exponential Random Variable -- Appendix 9. Index to Author-Created MATLAB m-Files in the Book -- Glossary -- Acknowledgments -- Index -- Also by Paul J. Nahin
18. Waiting for Stoplights
Appendix 5. An Illustration of the Inclusion-Exclusion Principle
ntroduction
Index
Appendix 1. One Way to Guess on a Test
8. A Toilet Paper Dilemma
15. How Long Is the Wait to Get the Potato Salad?
21. Chain Reactions, Branching Processes, and Baby Boys
Preface to the Paperback Edition
Acknowledgments
2. Will Lil and Bill Meet at the Malt Shop?
19. Electing Emperors and Popes
7. The Pipe Smoker’s Discovery
15. How Long Is theWait to Get the Potato Salad?
The Problems --
17. Waiting for Buses
20. An Optimal Stopping Problem
Also by Paul J. Nahin
9. The Forgetful Burglar Problem
11. The Case of the Missing Senators
Appendix 4. Solving Montmort’s Problem by Recursion
5. The Gamow-Stern Elevator Puzzle
Appendix 9. Author-Created MATLAB m-files and Their Location in the Book
Appendix 7. How to Simulate Kelvin’s Fair Coin with a Biased Coin
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/
1. The Clumsy Dishwasher Problem
Contents
Appendix 3. Random Harmonic Series
Appendix 6. Solutions to the Spin Game
6. Steve’s Elevator Problem
12. How Many Runners in a Marathon?
Glossary
Appendix 2. An Example of Variance Reduction in the Monte Carlo Method
Frontmatter --
14. Parrondo’s Paradox
16. The Appeals Court Paradox
Appendix 8. How to Simulate an Exponential Random Variable
3. A Parallel Parking Question
The Solutions --
4. A Curious Coin-Flipping Game
10. The Umbrella Quandary
13. A Police Patrol Problem