Problems and Snapshots from the World of Probability

1. Front Matter

   Pages i-xii

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2. Welcoming problems

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 1-12

3. Basic probability theory I

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 13-22

4. Basic probability theory II

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 23-32

5. Topics from early days I

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 33-43

6. Topics from early days II

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 44-61

7. Random permutations

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 62-78

8. Miscellaneous I

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 79-91

9. Poisson approximation

   • Gunnar Blom, Lars Holst, Dennis Sandell

   Pages 92-102

10. Miscellaneous II

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 103-114

11. Random walks

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 115-132

12. Urn models

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 133-145

13. Cover times

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 146-155

14. Markov chains

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 156-172

15. Patterns

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 173-185

16. Embedding procedures

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 186-198

17. Special topics

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 199-213

18. Farewell problems

    • Gunnar Blom, Lars Holst, Dennis Sandell

    Pages 214-229

19. Back Matter

    Pages 230-240

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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' were dexterous solvers of discrete problems. We hope that this pleasure will be transmitted to the readers. The first problem-book of a similar kind as ours is perhaps Mosteller's well-known Fifty Challenging Problems in Probability (1965). Possibly, our book is the second. The book contains 125 problems and snapshots from the world of prob­ ability. A 'problem' generally leads to a question with a definite answer. A 'snapshot' is either a picture or a bird's-eye view of some probabilistic field. The selection is, of course, highly subjective, and we have not even tried to cover all parts of the subject systematically. Limit theorems appear only seldom, for otherwise the book would have become unduly large. We want to state emphatically that we have not written a textbook in probability, but rather a book for browsing through when occupying an easy-chair. Therefore, ideas and results are often put forth without a machinery of formulas and derivations; the conscientious readers, who want to penetrate the whole clockwork, will soon have to move to their desks and utilize appropriate tools.

• Markov chain
• Martingale
• Poisson process
• Probability theory
• Random variable
• random walk

• Department of Mathematical Statistics, University of Lund, Lund, Sweden

  Gunnar Blom

• Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

  Lars Holst

• Department of Biostatistics and Data Processing, Astra Draco AB, Lund, Sweden

  Dennis Sandell

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