40 Puzzles and Problems in Probability and Mathematical Statistics

40 Puzzles and Problems in Probability and Mathematical Statistics......Page 1
Preface......Page 7
Contents......Page 9
Notation and Terminology......Page 13
A Tournament Problem......Page 15
How Often Do Head and Tail Occur Equally Often?......Page 16
Random Areas......Page 17
The Optimal Level of Supply......Page 18
Mixing RVs vs. Mixing Their Distributions......Page 19
Random Ranks......Page 20
Is 2X the Same as X1 + X2?......Page 21
Large Gaps......Page 22
ML Estimation with the Geometric Distribution......Page 23
The Lady Tasting Tea......Page 24
Approximately How Tall Is the Tallest?......Page 25
The Median in Samples of Exponential RVs......Page 26
Paradoxical Contribution......Page 27
Discrete Variables with Continuous Error......Page 28
The High-Resolution and the Black-White View......Page 29
The arcsin(p) Transform......Page 30
The Delta Technique with One Variable......Page 31
How Many Trials Produced a Given Maximum?......Page 32
Waiting for Success......Page 33
Mean Waiting Time for 1-1 vs. 1-2......Page 34
Random Areas......Page 35
Mixing RVs vs. Mixing Their Distributions......Page 36
Ups and Downs......Page 37
Random Powers of Random Variables......Page 38
How Many Twins Are Homozygotic?......Page 39
Approximately How Tall Is the Tallest?......Page 40
Breaking the Record......Page 41
The High-Resolution and the Black-White View......Page 42
Binomial Trials Depending on a Latent Variable......Page 43
The Delta Technique with Two Variables......Page 44
Waiting for Success......Page 45
To Begin or Not to Begin?......Page 46
A Tournament Problem......Page 47
Mean Waiting Time for 1-1 vs. 1-2......Page 48
How to Divide up Gains in Interrupted Games......Page 51
How Often Do Head and Tail Occur Equally Often?......Page 53
Sample Size vs. Signal Strength......Page 56
Birthday Holidays......Page 58
Random Areas......Page 60
Maximize Your Gain......Page 61
Maximize Your Gain When Losses Are Possible......Page 63
The Optimal Level of Supply......Page 65
Mixing RVs vs. Mixing Their Distributions......Page 67
Throwing the Same vs. Different Dice......Page 70
Random Ranks......Page 72
Ups and Downs......Page 73
Is 2X the Same as X1 + X2?......Page 74
How Many Donors Needed?......Page 75
Large Gaps......Page 77
Small Gaps......Page 78
Random Powers of Random Variables......Page 79
How Many Bugs Are Left?......Page 81
ML Estimation with the Geometric Distribution......Page 83
How Many Twins Are Homozygotic?......Page 86
The Lady Tasting Tea......Page 88
How to Aggregate Significance Levels......Page 91
Approximately How Tall Is the Tallest?......Page 93
The Range in Samples of Exponential RVs......Page 95
The Median in Samples of Exponential RVs......Page 97
Breaking the Record......Page 98
Paradoxical Contribution......Page 101
Attracting Mediocrity......Page 102
Discrete Variables with Continuous Error......Page 107
The High-Resolution and the Black-White View......Page 109
The Bivariate Lognormal......Page 114
The arcsin(p) Transform......Page 117
Binomial Trials Depending on a Latent Variable......Page 119
The Delta Technique with One Variable......Page 121
The Delta Technique with Two Variables......Page 123
How Many Trials Produced a Given Maximum?......Page 126
Waiting for Success......Page 129
References......Page 131
Index......Page 133