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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