40 Puzzles and Problems in Probability and Mathematical Statistics

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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