LEADER 05796nam 22006375 450 001 9910820402203321 005 20230905220111.0 010 $a1-4008-4611-0 010 $a1-299-13927-2 024 7 $a10.1515/9781400846115 035 $a(CKB)2550000001000524 035 $a(EBL)1105925 035 $a(OCoLC)832618068 035 $a(SSID)ssj0000906747 035 $a(PQKBManifestationID)11553696 035 $a(PQKBTitleCode)TC0000906747 035 $a(PQKBWorkID)10854719 035 $a(PQKB)10289647 035 $a(DE-B1597)447195 035 $a(OCoLC)834555589 035 $a(OCoLC)979905334 035 $a(DE-B1597)9781400846115 035 $a(MiAaPQ)EBC1105925 035 $a(EXLCZ)992550000001000524 100 $a20190708d2013 fg 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDigital Dice $eComputational Solutions to Practical Probability Problems /$fPaul J. Nahin 205 $aWith a New preface by the author 210 1$aPrinceton, NJ :$cPrinceton University Press,$d[2013] 210 4$dİ2013 215 $a1 online resource (289 p.) 225 0 $aPrinceton Puzzlers 300 $aDescription based upon print version of record. 311 $a0-691-15821-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter --$tContents --$tPreface to the Paperback Edition --$tIntroduction --$tThe Problems --$t1. The Clumsy Dishwasher Problem --$t2. Will Lil and Bill Meet at the Malt Shop? --$t3. A Parallel Parking Question --$t4. A Curious Coin-Flipping Game --$t5. The Gamow-Stern Elevator Puzzle --$t6. Steve's Elevator Problem --$t7. The Pipe Smoker's Discovery --$t8. A Toilet Paper Dilemma --$t9. The Forgetful Burglar Problem --$t10. The Umbrella Quandary --$t11. The Case of the Missing Senators --$t12. How Many Runners in a Marathon? --$t13. A Police Patrol Problem --$t14. Parrondo's Paradox --$t15. How Long Is the Wait to Get the Potato Salad? --$t16. The Appeals Court Paradox --$t17. Waiting for Buses --$t18. Waiting for Stoplights --$t19. Electing Emperors and Popes --$t20. An Optimal Stopping Problem --$t21. Chain Reactions, Branching Processes, and Baby Boys --$tThe Solutions --$t1. The Clumsy Dishwasher Problem --$t2. Will Lil and Bill Meet at the Malt Shop? --$t3. A Parallel Parking Question --$t4. A Curious Coin-Flipping Game --$t5. The Gamow-Stern Elevator Puzzle --$t6. Steve's Elevator Problem --$t7. The Pipe Smoker's Discovery --$t8. A Toilet Paper Dilemma --$t9. The Forgetful Burglar Problem --$t10. The Umbrella Quandary --$t11. The Case of the Missing Senators --$t12. How Many Runners in a Marathon? --$t13. A Police Patrol Problem --$t14. Parrondo's Paradox --$t15. How Long Is the Wait to Get the Potato Salad? --$t16. The Appeals Court Paradox --$t17. Waiting for Buses --$t18. Waiting for Stoplights --$t19. Electing Emperors and Popes --$t20. An Optimal Stopping Problem --$t21. Chain Reactions, Branching Processes, and Baby Boys --$tAppendix 1. One Way to Guess on a Test --$tAppendix 2. An Example of Variance Reduction in the Monte Carlo Method --$tAppendix 3. Random Harmonic Series --$tAppendix 4. Solving Montmort's Problem by Recursion --$tAppendix 5. An Illustration of the Inclusion-Exclusion Principle --$tAppendix 6. Solutions to the Spin Game --$tAppendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin --$tAppendix 8. How to Simulate an Exponential Random Variable --$tAppendix 9. Author-Created MATLAB m-files and Their Location in the Book --$tGlossary --$tAcknowledgments --$tIndex --$tAlso by Paul J. Nahin 330 $aSome probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition. 410 0$aPrinceton Puzzlers 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aMathematical Statistics$2HILCC 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aMathematical Statistics 676 $a519.2076 700 $aNahin$b Paul J.$048655 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910820402203321 996 $aDigital Dice$94108069 997 $aUNINA