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Problems and Snapshots from the World of Probability [[electronic resource] /] / by Gunnar Blom, Lars Holst, Dennis Sandell
| Problems and Snapshots from the World of Probability [[electronic resource] /] / by Gunnar Blom, Lars Holst, Dennis Sandell |
| Autore | Blom Gunnar |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 256 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities
Probability Theory and Stochastic Processes |
| ISBN | 1-4612-4304-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Welcoming problems -- 1.1 The friendly illiterate -- 1.2 Tourist with a short memory -- 1.3 The car and the goats -- 1.4 Patterns I -- 1.5 Classical random walk I -- 1.6 Number of walks until no shoes -- 1.7 Banach’s match box problem -- 1.8 The generous king -- 2. Basic probability theory I -- 2.1 Remarkable conditional probabilities -- 2.2 Exchangeability I -- 2.3 Exchangeability II -- 2.4 Combinations of events I -- 2.5 Problems concerning random numbers -- 2.6 Zero-one random variables I -- 3. Basic probability theory II -- 3.1 A trick for determining expectations -- 3.2 Probability generating functions -- 3.3 People at the corners of a triangle -- 3.4 Factorial generating functions -- 3.5 Zero-one random variables II -- 3.6 Combinations of events II -- 4. Topics from early days I -- 4.1 Cardano — a pioneer -- 4.2 Birth of probability -- 4.3 The division problem -- 4.4 Huygens’s second problem -- 4.5 Huygens’s fifth problem -- 4.6 Points when throwing several dice -- 4.7 Bernoulli and the game of tennis -- 5. Topics from early days II -- 5.1 History of some common distributions -- 5.2 Waldegrave’s problem I -- 5.3 Petersburg paradox -- 5.4 Rencontre I -- 5.5 Occupancy I -- 5.6 Stirling numbers of the second kind -- 5.7 Bayes’s theorem and Law of Succession -- 5.8 Ménage I -- 6. Random permutations -- 6.1 Runs I -- 6.2 Cycles in permutations -- 6.3 Stirling numbers of the first kind -- 6.4 Ascents in permutations -- 6.5 Eulerian numbers -- 6.6 Exceedances in permutations -- 6.7 Price fluctuations -- 6.8 Oscillations I -- 6.9 Oscillations II -- 7. Miscellaneous I -- 7.1 Birthdays -- 7.2 Poker -- 7.3 Negative binomial -- 7.4 Negative hypergeometric I -- 7.5 Coupon collecting I -- 7.6 Coupon collecting II -- 7.7 Ménage II -- 7.8 Rencontre II -- 8. Poisson approximation -- 8.1 Similar pairs and triplets -- 8.2 A Lotto problem -- 8.3 Variation distance -- 8.4 Poisson-binomial -- 8.5 Rencontre III -- 8.6 Ménage III -- 8.7 Occupancy II -- 9. Miscellaneous II -- 9.1 Birthdays and similar triplets -- 9.2 Comparison of random numbers -- 9.3 Grouping by random division -- 9.4 Records I -- 9.5 Records II -- 9.6 A modification of blackjack -- 10. Random walks -- 10.1 Introduction -- 10.2 Classical random walk II -- 10.3 One absorbing barrier -- 10.4 The irresolute spider -- 10.5 Stars I -- 10.6 Closed stopping region -- 10.7 The reflection principle -- 10.8 Ballot problem -- 10.9 Range of a random walk -- 11. Urn models -- 11.1 Randomly filled urn -- 11.2 Pólya’s model I -- 11.3 Pólya’s model II -- 11.4 Pólya’s model III -- 11.5 Ehrenfest’s model I -- 11.6 Ehrenfest’s game -- 11.7 A pill problem -- 12. Cover times -- 12.1 Introduction -- 12.2 Complete graph -- 12.3 Linear finite graph -- 12.4 Polygon -- 12.5 A false conjecture -- 12.6 Stars II -- 12.7 Inequality for cover times -- 13. Markov chains -- 13.1 Review I -- 13.2 Review II -- 13.3 Random walk: two reflecting barriers -- 13.4 Ehrenfest’s model II -- 13.5 Doubly stochastic transition matrix -- 13.6 Card shuffling -- 13.7 Transition times for Markov chains -- 13.8 Reversible Markov chains -- 13.9 Markov chains with homesickness -- 14. Patterns -- 14.1 Runs II -- 14.2 Patterns II -- 14.3 Patterns III -- 14.4 A game for pirates -- 14.5 Penney’s game -- 14.6 Waldegrave’s problem II -- 14.7 How many patterns? -- 15. Embedding procedures -- 15.1 Drawings with replacement -- 15.2 Repetition of colours -- 15.3 Birthdays revisited -- 15.4 Coupon collecting III -- 15.5 Drawings without replacement -- 15.6 Socks in the laundry -- 15.7 Negative hypergeometric II -- 15.8 The first-to-r game I -- 16. Special topics -- 16.1 Exchangeability III -- 16.2 Martingales -- 16.3 Wald’s equation -- 16.4 Birth control -- 16.5 The r-heads-in-advance game -- 16.6 Patterns IV -- 16.7 Random permutation of 1’s and (?1)’s -- 17. Farewell problems -- 17.1 The first-to-r game II -- 17.2 Random walk on a chessboard -- 17.3 Game with disaster -- 17.4 A rendezvous problem -- 17.5 Modified coin-tossing -- 17.6 Palindromes -- References. |
| Record Nr. | UNINA-9910480707203321 |
Blom Gunnar
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Snapshots from the World of Probability [[electronic resource] /] / by Gunnar Blom, Lars Holst, Dennis Sandell
| Problems and Snapshots from the World of Probability [[electronic resource] /] / by Gunnar Blom, Lars Holst, Dennis Sandell |
| Autore | Blom Gunnar |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 256 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities
Probability Theory and Stochastic Processes |
| ISBN | 1-4612-4304-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Welcoming problems -- 1.1 The friendly illiterate -- 1.2 Tourist with a short memory -- 1.3 The car and the goats -- 1.4 Patterns I -- 1.5 Classical random walk I -- 1.6 Number of walks until no shoes -- 1.7 Banach’s match box problem -- 1.8 The generous king -- 2. Basic probability theory I -- 2.1 Remarkable conditional probabilities -- 2.2 Exchangeability I -- 2.3 Exchangeability II -- 2.4 Combinations of events I -- 2.5 Problems concerning random numbers -- 2.6 Zero-one random variables I -- 3. Basic probability theory II -- 3.1 A trick for determining expectations -- 3.2 Probability generating functions -- 3.3 People at the corners of a triangle -- 3.4 Factorial generating functions -- 3.5 Zero-one random variables II -- 3.6 Combinations of events II -- 4. Topics from early days I -- 4.1 Cardano — a pioneer -- 4.2 Birth of probability -- 4.3 The division problem -- 4.4 Huygens’s second problem -- 4.5 Huygens’s fifth problem -- 4.6 Points when throwing several dice -- 4.7 Bernoulli and the game of tennis -- 5. Topics from early days II -- 5.1 History of some common distributions -- 5.2 Waldegrave’s problem I -- 5.3 Petersburg paradox -- 5.4 Rencontre I -- 5.5 Occupancy I -- 5.6 Stirling numbers of the second kind -- 5.7 Bayes’s theorem and Law of Succession -- 5.8 Ménage I -- 6. Random permutations -- 6.1 Runs I -- 6.2 Cycles in permutations -- 6.3 Stirling numbers of the first kind -- 6.4 Ascents in permutations -- 6.5 Eulerian numbers -- 6.6 Exceedances in permutations -- 6.7 Price fluctuations -- 6.8 Oscillations I -- 6.9 Oscillations II -- 7. Miscellaneous I -- 7.1 Birthdays -- 7.2 Poker -- 7.3 Negative binomial -- 7.4 Negative hypergeometric I -- 7.5 Coupon collecting I -- 7.6 Coupon collecting II -- 7.7 Ménage II -- 7.8 Rencontre II -- 8. Poisson approximation -- 8.1 Similar pairs and triplets -- 8.2 A Lotto problem -- 8.3 Variation distance -- 8.4 Poisson-binomial -- 8.5 Rencontre III -- 8.6 Ménage III -- 8.7 Occupancy II -- 9. Miscellaneous II -- 9.1 Birthdays and similar triplets -- 9.2 Comparison of random numbers -- 9.3 Grouping by random division -- 9.4 Records I -- 9.5 Records II -- 9.6 A modification of blackjack -- 10. Random walks -- 10.1 Introduction -- 10.2 Classical random walk II -- 10.3 One absorbing barrier -- 10.4 The irresolute spider -- 10.5 Stars I -- 10.6 Closed stopping region -- 10.7 The reflection principle -- 10.8 Ballot problem -- 10.9 Range of a random walk -- 11. Urn models -- 11.1 Randomly filled urn -- 11.2 Pólya’s model I -- 11.3 Pólya’s model II -- 11.4 Pólya’s model III -- 11.5 Ehrenfest’s model I -- 11.6 Ehrenfest’s game -- 11.7 A pill problem -- 12. Cover times -- 12.1 Introduction -- 12.2 Complete graph -- 12.3 Linear finite graph -- 12.4 Polygon -- 12.5 A false conjecture -- 12.6 Stars II -- 12.7 Inequality for cover times -- 13. Markov chains -- 13.1 Review I -- 13.2 Review II -- 13.3 Random walk: two reflecting barriers -- 13.4 Ehrenfest’s model II -- 13.5 Doubly stochastic transition matrix -- 13.6 Card shuffling -- 13.7 Transition times for Markov chains -- 13.8 Reversible Markov chains -- 13.9 Markov chains with homesickness -- 14. Patterns -- 14.1 Runs II -- 14.2 Patterns II -- 14.3 Patterns III -- 14.4 A game for pirates -- 14.5 Penney’s game -- 14.6 Waldegrave’s problem II -- 14.7 How many patterns? -- 15. Embedding procedures -- 15.1 Drawings with replacement -- 15.2 Repetition of colours -- 15.3 Birthdays revisited -- 15.4 Coupon collecting III -- 15.5 Drawings without replacement -- 15.6 Socks in the laundry -- 15.7 Negative hypergeometric II -- 15.8 The first-to-r game I -- 16. Special topics -- 16.1 Exchangeability III -- 16.2 Martingales -- 16.3 Wald’s equation -- 16.4 Birth control -- 16.5 The r-heads-in-advance game -- 16.6 Patterns IV -- 16.7 Random permutation of 1’s and (?1)’s -- 17. Farewell problems -- 17.1 The first-to-r game II -- 17.2 Random walk on a chessboard -- 17.3 Game with disaster -- 17.4 A rendezvous problem -- 17.5 Modified coin-tossing -- 17.6 Palindromes -- References. |
| Record Nr. | UNINA-9910789222603321 |
|
Blom Gunnar
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Snapshots from the World of Probability / / by Gunnar Blom, Lars Holst, Dennis Sandell
| Problems and Snapshots from the World of Probability / / by Gunnar Blom, Lars Holst, Dennis Sandell |
| Autore | Blom Gunnar |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (XII, 256 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities
Probability Theory |
| ISBN | 1-4612-4304-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Welcoming problems -- 1.1 The friendly illiterate -- 1.2 Tourist with a short memory -- 1.3 The car and the goats -- 1.4 Patterns I -- 1.5 Classical random walk I -- 1.6 Number of walks until no shoes -- 1.7 Banach’s match box problem -- 1.8 The generous king -- 2. Basic probability theory I -- 2.1 Remarkable conditional probabilities -- 2.2 Exchangeability I -- 2.3 Exchangeability II -- 2.4 Combinations of events I -- 2.5 Problems concerning random numbers -- 2.6 Zero-one random variables I -- 3. Basic probability theory II -- 3.1 A trick for determining expectations -- 3.2 Probability generating functions -- 3.3 People at the corners of a triangle -- 3.4 Factorial generating functions -- 3.5 Zero-one random variables II -- 3.6 Combinations of events II -- 4. Topics from early days I -- 4.1 Cardano — a pioneer -- 4.2 Birth of probability -- 4.3 The division problem -- 4.4 Huygens’s second problem -- 4.5 Huygens’s fifth problem -- 4.6 Points when throwing several dice -- 4.7 Bernoulli and the game of tennis -- 5. Topics from early days II -- 5.1 History of some common distributions -- 5.2 Waldegrave’s problem I -- 5.3 Petersburg paradox -- 5.4 Rencontre I -- 5.5 Occupancy I -- 5.6 Stirling numbers of the second kind -- 5.7 Bayes’s theorem and Law of Succession -- 5.8 Ménage I -- 6. Random permutations -- 6.1 Runs I -- 6.2 Cycles in permutations -- 6.3 Stirling numbers of the first kind -- 6.4 Ascents in permutations -- 6.5 Eulerian numbers -- 6.6 Exceedances in permutations -- 6.7 Price fluctuations -- 6.8 Oscillations I -- 6.9 Oscillations II -- 7. Miscellaneous I -- 7.1 Birthdays -- 7.2 Poker -- 7.3 Negative binomial -- 7.4 Negative hypergeometric I -- 7.5 Coupon collecting I -- 7.6 Coupon collecting II -- 7.7 Ménage II -- 7.8 Rencontre II -- 8. Poisson approximation -- 8.1 Similar pairs and triplets -- 8.2 ALotto problem -- 8.3 Variation distance -- 8.4 Poisson-binomial -- 8.5 Rencontre III -- 8.6 Ménage III -- 8.7 Occupancy II -- 9. Miscellaneous II -- 9.1 Birthdays and similar triplets -- 9.2 Comparison of random numbers -- 9.3 Grouping by random division -- 9.4 Records I -- 9.5 Records II -- 9.6 A modification of blackjack -- 10. Random walks -- 10.1 Introduction -- 10.2 Classical random walk II -- 10.3 One absorbing barrier -- 10.4 The irresolute spider -- 10.5 Stars I -- 10.6 Closed stopping region -- 10.7 The reflection principle -- 10.8 Ballot problem -- 10.9 Range of a random walk -- 11. Urn models -- 11.1 Randomly filled urn -- 11.2 Pólya’s model I -- 11.3 Pólya’s model II -- 11.4 Pólya’s model III -- 11.5 Ehrenfest’s model I -- 11.6 Ehrenfest’s game -- 11.7 A pill problem -- 12. Cover times -- 12.1 Introduction -- 12.2 Complete graph -- 12.3 Linear finite graph -- 12.4 Polygon -- 12.5 A false conjecture -- 12.6 Stars II -- 12.7 Inequality for cover times -- 13. Markov chains -- 13.1 Review I -- 13.2 Review II -- 13.3 Random walk: two reflecting barriers -- 13.4 Ehrenfest’s model II -- 13.5 Doubly stochastic transition matrix -- 13.6 Card shuffling -- 13.7 Transition times for Markov chains -- 13.8 Reversible Markov chains -- 13.9 Markov chains with homesickness -- 14. Patterns -- 14.1 Runs II -- 14.2 Patterns II -- 14.3 Patterns III -- 14.4 A game for pirates -- 14.5 Penney’s game -- 14.6 Waldegrave’s problem II -- 14.7 How many patterns? -- 15. Embedding procedures -- 15.1 Drawings with replacement -- 15.2 Repetition of colours -- 15.3 Birthdays revisited -- 15.4 Coupon collecting III -- 15.5 Drawings without replacement -- 15.6 Socks in the laundry -- 15.7 Negative hypergeometric II -- 15.8 The first-to-r game I -- 16. Special topics -- 16.1 Exchangeability III -- 16.2 Martingales -- 16.3 Wald’s equation.-16.4 Birth control -- 16.5 The r-heads-in-advance game -- 16.6 Patterns IV -- 16.7 Random permutation of 1’s and (?1)’s -- 17. Farewell problems -- 17.1 The first-to-r game II -- 17.2 Random walk on a chessboard -- 17.3 Game with disaster -- 17.4 A rendezvous problem -- 17.5 Modified coin-tossing -- 17.6 Palindromes -- References. |
| Record Nr. | UNINA-9910962007303321 |
|
Blom Gunnar
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||