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40 Puzzles and Problems in Probability and Mathematical Statistics (Problem Books in Mathematics)by Wolfgang Schwarz
Synopses & ReviewsPublisher Comments:"40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, nonstandard 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 plainstyle 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 nonstandard aspect or an approach which is not immediately obvious. The word puzzles in the title refers to questions in which some qualitative, nontechnical 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 stateoftheart 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 selfstudy, the author has included very detailed stepforstep solutions of all problems and also short hints which point the reader in the appropriate direction.
Synopsis:Many puzzles and problems presented here are either new within a problem solving context or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources.
Synopsis:This book is based on the view that cognitive skills are best acquired by solving challenging, nonstandard probability problems. Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are 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 will be a handy resource for professors looking for problems to assign, for undergraduate math students, and for a more general audience of amateur scientists.
Table of ContentsPreface. Notation and Terminology. Problems. Hints. Solutions. References. Index.
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