40 Puzzles and Problems in Probability and Mathematical Statistics

ISBN-13: 9781441925220 / Angielski / Miękka / 2010 / 124 str.

Wolfgang Schwarz

Opis

As a student I discovered in our library a thin booklet by Frederick Mosteller entitled50 Challenging Problems in Probability. Itreferredtoas- plementary regular textbook by William Feller, An Introduction to Pro- bilityTheoryanditsApplications.SoItookthisonealong, too, andstartedon the ?rst of Mosteller s problems on the train riding home. From that evening, I caught on to probability. These two books were not primarily about abstract formalisms but rather about basic modeling ideas and about ways often extremely elegant ones to apply those notions to a surprising variety of empirical phenomena. Essentially, these books taught the reader the skill to think probabilistically and to apply simple probability models to real-world problems. The present book is in this tradition; it is based on the view that those cognitive skills are best acquired by solving challenging, nonstandard pro- bility problems. My own experience, both in learning and in teaching, is that challenging problems often help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts."

Recenzje

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)

Spis treści

Problems.- Hints.- Solutions.

O autorze

The present book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are of course long known) or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources which in this case are generally given. This book contains far more problems of a statistical nature than the competition. It will become a handy resource for professors looking for problems to assign for a course, and will be of interest to undergraduate math students, as well as a more general audience of amateur scientists.

Blurb

"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.