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Problems and Snapshots from the World of Probability

We, the authors of this book, are three ardent devotees of chance, or some­ what more precisely, of discrete probability. When we were collecting the material, we felt that one special pleasure of the field lay in its evocation of an earlier age: many of our 'probabilistic forefathers' wer...

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Bibliographic Details
Main Authors: Blom, Gunnar, Holst, Lars (Author), Sandell, Dennis (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1994, 1994
Edition:1st ed. 1994
Subjects:
Probability Theory
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 17.4 A rendezvous problem
  • 17.5 Modified coin-tossing
  • 17.6 Palindromes
  • References
  • 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
  • 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
  • 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

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