40 Puzzles and Problems in Probability and Mathematical Statistics

✍ Scribed by Wolfgang Schwarz

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 134
• Series: Problem Books in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

The present book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. The author's own experience, both in learning and in teaching, is that challenging problems often provide more, and longer lasting, inductive insights than plain-style deductions from general concepts. Problems help to develop, and to sharpen our intuition for important probabilistical concepts and tools such as conditionaing or first-step analyses.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.

✦ Table of Contents

front-matter......Page 1
Notation and Terminology......Page 8
A Tournament Problem......Page 13
How Often Do Head and Tail Occur Equally Often?......Page 14
Random Areas......Page 15
The Optimal Level of Supply......Page 16
Mixing RVs vs. Mixing Their Distributions......Page 17
Random Ranks......Page 18
Is 2X the Same as X1 + X2?......Page 19
Large Gaps......Page 20
ML Estimation with the Geometric Distribution......Page 21
The Lady Tasting Tea......Page 22
Approximately How Tall Is the Tallest?......Page 23
The Median in Samples of Exponential RVs......Page 24
Paradoxical Contribution......Page 25
Discrete Variables with Continuous Error......Page 26
The High-Resolution and the Black-White View......Page 27
The arcsin(p) Transform......Page 28
The Delta Technique with One Variable......Page 29
How Many Trials Produced a Given Maximum?......Page 30
Waiting for Success......Page 31
Mean Waiting Time for 1-1 vs. 1-2......Page 32
Random Areas......Page 33
Mixing RVs vs. Mixing Their Distributions......Page 34
Ups and Downs......Page 35
Random Powers of Random Variables......Page 36
How Many Twins Are Homozygotic?......Page 37
Approximately How Tall Is the Tallest?......Page 38
Breaking the Record......Page 39
The High-Resolution and the Black-White View......Page 40
Binomial Trials Depending on a Latent Variable......Page 41
The Delta Technique with Two Variables......Page 42
Waiting for Success......Page 43
To Begin or Not to Begin?......Page 44
A Tournament Problem......Page 45
Mean Waiting Time for 1-1 vs. 1-2......Page 46
How to Divide up Gains in Interrupted Games......Page 49
How Often Do Head and Tail Occur Equally Often?......Page 51
Sample Size vs. Signal Strength......Page 54
Birthday Holidays......Page 56
Random Areas......Page 58
Maximize Your Gain......Page 59
Maximize Your Gain When Losses Are Possible......Page 61
The Optimal Level of Supply......Page 63
Mixing RVs vs. Mixing Their Distributions......Page 65
Throwing the Same vs. Different Dice......Page 68
Random Ranks......Page 70
Ups and Downs......Page 71
Is 2X the Same as X1 + X2?......Page 72
How Many Donors Needed?......Page 73
Large Gaps......Page 75
Small Gaps......Page 76
Random Powers of Random Variables......Page 77
How Many Bugs Are Left?......Page 79
ML Estimation with the Geometric Distribution......Page 81
How Many Twins Are Homozygotic?......Page 84
The Lady Tasting Tea......Page 86
How to Aggregate Significance Levels......Page 89
Approximately How Tall Is the Tallest?......Page 91
The Range in Samples of Exponential RVs......Page 93
The Median in Samples of Exponential RVs......Page 95
Breaking the Record......Page 96
Paradoxical Contribution......Page 99
Attracting Mediocrity......Page 100
Discrete Variables with Continuous Error......Page 105
The High-Resolution and the Black-White View......Page 107
The Bivariate Lognormal......Page 112
The arcsin(p) Transform......Page 115
Binomial Trials Depending on a Latent Variable......Page 117
The Delta Technique with One Variable......Page 119
The Delta Technique with Two Variables......Page 121
How Many Trials Produced a Given Maximum?......Page 124
Waiting for Success......Page 127
References......Page 129
Index......Page 131