40 Puzzles and Problems in Probability and Mathematical Statistics

front-matter
Notation and Terminology
01Problems
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
02Hints
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
03Solutions
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
back-matter
References
Index