**40 Puzzles and Problems in Probability and Mathematical Statistics by Wolf Schwarz, ISBN-13: 978-0387735115**

[PDF eBook eTextbook]

- Publisher: Springer; 2008th edition (November 30, 2007)
- Language: English
- 136 pages
- ISBN-10: 0387735119
- ISBN-13: 978-0387735115

This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems.

* “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.

**Table of Contents:**

Notation and Terminology

Problems

To Begin or Not to Begin?

A Tournament Problem

Mean Waiting Time for 1-1 vs. 1-2

How to Divide up Gains in Interrupted Games

How Often Do Head and Tail Occur Equally Often?

Sample Size vs. Signal Strength

Birthday Holidays

Random Areas

Maximize Your Gain

Maximize Your Gain When Losses Are Possible

The Optimal Level of Supply

Mixing RVs vs. Mixing Their Distributions

Throwing the Same vs. Different Dice

Random Ranks

Ups and Downs

Is 2X the Same as X1 + X2?

How Many Donors Needed?

Large Gaps

Small Gaps

Random Powers of Random Variables

How Many Bugs Are Left?

ML Estimation with the Geometric Distribution

How Many Twins Are Homozygotic?

The Lady Tasting Tea

How to Aggregate Significance Levels

Approximately How Tall Is the Tallest?

The Range in Samples of Exponential RVs

The Median in Samples of Exponential RVs

Breaking the Record

Paradoxical Contribution

Attracting Mediocrity

Discrete Variables with Continuous Error

The High-Resolution and the Black-White View

The Bivariate Lognormal

The arcsin(p) Transform

Binomial Trials Depending on a Latent Variable

The Delta Technique with One Variable

The Delta Technique with Two Variables

How Many Trials Produced a Given Maximum?

Waiting for Success

Hints

To Begin or Not to Begin?

A Tournament Problem

Mean Waiting Time for 1-1 vs. 1-2

How to Divide up Gains in Interrupted Games

How Often Do Head and Tail Occur Equally Often?

Sample Size vs. Signal Strength

Birthday Holidays

Random Areas

Maximize Your Gain

Maximize Your Gain When Losses Are Possible

The Optimal Level of Supply

Mixing RVs vs. Mixing Their Distributions

Throwing the Same vs. Different Dice

Random Ranks

Ups and Downs

Is 2X the Same as X1 + X2?

How Many Donors Needed?

Large Gaps

Small Gaps

Random Powers of Random Variables

How Many Bugs Are Left?

ML Estimation with the Geometric Distribution

How Many Twins Are Homozygotic?

The Lady Tasting Tea

How to Aggregate Significance Levels

Approximately How Tall Is the Tallest?

The Range in Samples of Exponential RVs

The Median in Samples of Exponential RVs

Breaking the Record

Paradoxical Contribution

Attracting Mediocrity

Discrete Variables with Continuous Error

The High-Resolution and the Black-White View

The Bivariate Lognormal

The arcsin(p) Transform

Binomial Trials Depending on a Latent Variable

The Delta Technique with One Variable

The Delta Technique with Two Variables

How Many Trials Produced a Given Maximum?

Waiting for Success

Solutions

To Begin or Not to Begin?

A Tournament Problem

Mean Waiting Time for 1-1 vs. 1-2

How to Divide up Gains in Interrupted Games

How Often Do Head and Tail Occur Equally Often?

Sample Size vs. Signal Strength

Birthday Holidays

Random Areas

Maximize Your Gain

Maximize Your Gain When Losses Are Possible

The Optimal Level of Supply

Mixing RVs vs. Mixing Their Distributions

Throwing the Same vs. Different Dice

Random Ranks

Ups and Downs

Is 2X the Same as X1 + X2?

How Many Donors Needed?

Large Gaps

Small Gaps

Random Powers of Random Variables

How Many Bugs Are Left?

ML Estimation with the Geometric Distribution

How Many Twins Are Homozygotic?

The Lady Tasting Tea

How to Aggregate Significance Levels

Approximately How Tall Is the Tallest?

The Range in Samples of Exponential RVs

The Median in Samples of Exponential RVs

Breaking the Record

Paradoxical Contribution

Attracting Mediocrity

Discrete Variables with Continuous Error

The High-Resolution and the Black-White View

The Bivariate Lognormal

The arcsin(p) Transform

Binomial Trials Depending on a Latent Variable

The Delta Technique with One Variable

The Delta Technique with Two Variables

How Many Trials Produced a Given Maximum?

Waiting for Success

References

Index

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