© 2008

40 Puzzles and Problems in Probability and Mathematical Statistics


Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Wolfgang Schwarz
    Pages 1-21
  3. Wolfgang Schwarz
    Pages 23-34
  4. Wolfgang Schwarz
    Pages 35-119
  5. Back Matter
    Pages 121-122

About this book


"40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, non-standard probability problems. The motivation for this clearly written collection lies in the belief that challenging problems help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The selected problems fall into two broad categories. Problems related to probability theory come first, followed by problems related to the application of probability to the field of mathematical statistics. All problems seek to convey a non-standard aspect or an approach which is not immediately obvious.


The word puzzles in the title refers to questions in which some qualitative, non-technical insight is most important. Ideally, puzzles can teach a productive new way of framing or representing a given situation. Although the border between the two is not always clearly defined, problems tend to require a more systematic application of formal tools, and to stress more technical aspects. Thus, a major aim of the present collection is to bridge the gap between introductory texts and rigorous state-of-the-art books.


Anyone with a basic knowledge of probability, calculus and statistics will benefit from this book; however, many of the problems collected require little more than elementary probability and straight logical reasoning. To assist anyone using this book for self-study, the author has included very detailed step-for-step solutions of all problems and also short hints which point the reader in the appropriate direction.


Variation mathematical statistics probability statistics

Authors and affiliations

  1. 1.Humanwissenschaftliche FakultätUniversität PotsdamD-14476 Potsdam-GolmGermany

Bibliographic information

  • Book Title 40 Puzzles and Problems in Probability and Mathematical Statistics
  • Authors Wolf Schwarz
  • Series Title Problem Books in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-73511-5
  • Softcover ISBN 978-1-4419-2522-0
  • eBook ISBN 978-0-387-73512-2
  • Series ISSN 0941-3502
  • Edition Number 1
  • Number of Pages XII, 124
  • Number of Illustrations 29 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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From the reviews:

"Wolfgang Schwarz’s collection of 40 problems, hints for approaching them, and their solutions is a genuinely valuable resource for the experienced (and not-so-experienced) probability teacher. … There are … problems, all potentially useful to anyone teaching probability and mathematical statistics. The difficulty level ranges nicely from elementary to sophisticated, so most readers will find something challenging here." (Mark Bollman, MathDL, January, 2008)

"In this work, Schwarz … provides a collection of problems involving probability theory and mathematical statistics. … This book may be of interest to advanced students studying probability theory. … Summing Up: Recommended. Libraries serving upper-division undergraduates and graduate students." (B. Borchers, Choice, Vol. 46 (6), February, 2009)

"It contains an eclectic selection of problems from a reasonably wide range of topics in probability and statistics … . In brief, this is an enjoyable book that is to be recommended to anyone looking for a very concise collection of good and interesting problems and puzzles in these subjects." (David Stirzaker, Siam Review, Vol. 51 (1), 2009)