Résumé
This introduction to elementary probability theory is
intended to serve as a pocketbook for applied
statisticians. It uses basic concepts for solving problems
collected from many books and journals. While most are very
new, some of the problems presented have a long history,
yet have been solved only recently.
Table of Contents
| Preface | xvii | |
| Acknowledgments | xix | |
| Introduction | xxi | |
| 1 | Probability | 1 |
| 1.1 | Introduction | 1 |
| 1.2 | Classical probability | 3 |
| 1.3 | Geometric probability | 8 |
| 1.4 | Dependence and independence | 10 |
| 1.5 | Bayes' theorem | 13 |
| 1.6 | Medical diagnostics | 15 |
| 1.7 | Random variables | 19 |
| 1.8 | Mang Kung dice game | 22 |
| 1.9 | Some discrete distributions | 24 |
| 1.10 | Some continuous distributions | 26 |
| 2 | Random walk | 29 |
| 2.1 | Gambler's ruin | 29 |
| 2.2 | American roulette | 32 |
| 2.3 | A reluctant random walk | 34 |
| 2.4 | Random walk until no shoes are available | 38 |
| 2.5 | Three-tower problem | 39 |
| 2.6 | Gambler's ruin problem with ties | 41 |
| 2.7 | Problem of prize division | 43 |
| 2.8 | Tennis | 47 |
| 2.9 | Wolf and sheep | 50 |
| 3 | Principle of reflection | 53 |
| 3.1 | Ticket-selling automat | 53 |
| 3.2 | Known structure of the queue | 54 |
| 3.3 | Queue with random structure | 57 |
| 3.4 | Random number of customers | 59 |
| 4 | Records | 63 |
| 4.1 | Records, probability, and statistics | 63 |
| 4.2 | Expected number of records | 64 |
| 4.3 | Probability of r records | 66 |
| 4.4 | Stirling numbers | 68 |
| 4.5 | Indicators | 70 |
| 4.6 | When records occur | 72 |
| 4.7 | Temperature records in Prague | 74 |
| 4.8 | How long we wait for the next record | 75 |
| 4.9 | Some applications of records | 78 |
| 5 | Problems that concern waiting | 79 |
| 5.1 | Geometric distribution | 79 |
| 5.2 | Problem about keys | 83 |
| 5.3 | Collection problems | 84 |
| 5.4 | When two players wait for a success | 86 |
| 5.5 | Waiting for a series of identical events | 86 |
| 5.6 | Lunch | 87 |
| 5.7 | Waiting student | 89 |
| 5.8 | Waiting for a bus in a town | 90 |
| 6 | Problems that concern optimization | 93 |
| 6.1 | Analysis of blood | 93 |
| 6.2 | Overbooking airline flights | 95 |
| 6.3 | Secretary problem | 97 |
| 6.4 | A birthday is not a workday | 100 |
| 6.5 | Voting | 100 |
| 6.6 | Dice without transitivity | 103 |
| 6.7 | How to increase reliability | 105 |
| 6.8 | Exam taking strategy | 110 |
| 6.9 | Two unknown numbers | 113 |
| 6.10 | Archers | 115 |
| 6.11 | A stacking problem | 115 |
| 6.12 | No risk, no win | 117 |
| 7 | Problems on calculating probability | 119 |
| 7.1 | Dormitory | 119 |
| 7.2 | Too many marriages | 123 |
| 7.3 | Tossing coins until all show heads | 124 |
| 7.4 | Anglers | 126 |
| 7.5 | Birds | 127 |
| 7.6 | Sultan and Caliph | 129 |
| 7.7 | Penalties | 130 |
| 7.8 | Two 6s and two 5s | 131 |
| 7.9 | Principle of inclusion and exclusion | 132 |
| 7.10 | More heads on coins | 133 |
| 7.11 | How combinatorial identities are born | 134 |
| 7.12 | Exams | 135 |
| 7.13 | Wyverns | 136 |
| 7.14 | Gaps among balls | 137 |
| 7.15 | Numbered pegs | 139 |
| 7.16 | Crux Mathematicorum | 140 |
| 7.17 | Ties in elections | 141 |
| 7.18 | Craps | 143 |
| 7.19 | Problem of exceeding 12 | 144 |
| 8 | Problems on calculating expectation | 147 |
| 8.1 | Christmas party | 147 |
| 8.2 | Spaghetti | 149 |
| 8.3 | Elevator | 151 |
| 8.4 | Matching pairs of socks | 152 |
| 8.5 | A guessing game | 153 |
| 8.6 | Expected number of draws | 155 |
| 8.7 | Length of the wire | 156 |
| 8.8 | Ancient Jewish game | 158 |
| 8.9 | Expected value of the smallest element | 160 |
| 8.10 | Ballot count | 161 |
| 8.11 | Bernoulli problem | 164 |
| 8.12 | Equal numbers of heads and tails | 165 |
| 8.13 | Pearls | 166 |
| 9 | Problems on statistical methods | 169 |
| 9.1 | Proofreading | 169 |
| 9.2 | How to enhance the accuracy of a measurement | 171 |
| 9.3 | How to determine the area of a square | 172 |
| 9.4 | Two routes to the airport | 175 |
| 9.5 | Christmas inequality | 178 |
| 9.6 | Cinderella | 180 |
| 10 | The LAD method | 185 |
| 10.1 | Median | 185 |
| 10.2 | Least squares method | 186 |
| 10.3 | LAD method | 188 |
| 10.4 | Laplace method | 189 |
| 10.5 | General straight line | 190 |
| 10.6 | LAD method in a general case | 191 |
| 11 | Probability in mathematics | 195 |
| 11.1 | Quadratic equations | 195 |
| 11.2 | Sum and product of random numbers | 198 |
| 11.3 | Socks and number theory | 201 |
| 11.4 | Tshebyshev problem | 203 |
| 11.5 | Random triangle | 205 |
| 11.6 | Lattice-point triangles | 209 |
| 12 | Matrix games | 211 |
| 12.1 | Linear programming | 211 |
| 12.2 | Pure strategies | 213 |
| 12.3 | Mixed strategies | 215 |
| 12.4 | Solution of matrix games | 216 |
| 12.5 | Solution of 2 [times] 2 games | 218 |
| 12.6 | Two-finger mora | 219 |
| 12.7 | Three-finger mora | 220 |
| 12.8 | Problem of colonel Blotto | 220 |
| 12.9 | Scissors--paper--stone | 221 |
| 12.10 | Birthday | 222 |
| References | 223 | |
| Topic Index | 231 | |
| Author Index | 234 |
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Wiley |
| Auteur(s) | Andel Jiri |
| Parution | 01/02/2001 |
| Nb. de pages | 234 |
| Format | 15,4 x 23,4 |
| Couverture | Broché |
| Poids | 468g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780471410898 |
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