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## Understanding probability: chance rules in everyday life

Author: Tijms, Henk C. Publisher: Cambridge University Press (CUP) 2007.Edition: 2nd ed.Language: EnglishDescription: 442 p. : Graphs/Ill. ; 23 cm.ISBN: 9780521701723Type of document: BookBibliography/Index: Includes bibliographical references and index
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Europe Campus
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Print QA273 .T55 2007
(Browse shelf)
001198401
Available 001198401
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Includes bibliographical references and index

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Understanding Probability Chance Rules in Everyday Life Contents Preface Introduction PART ONE: PROBABILITY IN ACTION 1 Probability questions page ix 1 9 11 17 18 27 32 37 39 41 44 50 55 64 73 74 79 82 86 89 93 95 2 The law of large numbers and simulation 2.1 The law of large numbers for probabilities 2.2 Basic probability concepts 2.3 Expected value and the law of large numbers 2.4 The drunkard's walk 2.5 The St. Petersburg paradox 2.6 Roulette and the law of large numbers 2.7 The Kelly betting system 2.8 Random-number generator 2.9 Simulating from probability distributions 2.10 Problems 3 Probabilities in everyday life 3.1 The birthday problem 3.2 The coupon collector's problem 3.3 Craps 3.4 Gambling systems for roulette 3.5 The 1970 draft lottery 3.6 Bootstrap method 3.7 Problems 4 Rare events and lotteries 4.1 The binomial distribution 4.2 The Poisson distribution 4.3 The hypergeometric distribution 4.4 Problems 5 Probability and statistics 5.1 The normal curve 5.2 The concept of standard deviation 5.3 The square-root law 5.4 The central limit theorem 5.5 Graphical illustration of the central limit theorem 5.6 Statistical applications 5.7 Confidence intervals for simulations 5.8 The central limit theorem and random walks 5.9 Falsified data and Benford's law 5.10 The normal distribution strikes again 5.11 Statistics and probability theory 5.12 Problems 6 Chance trees and Bayes' rule 6.1 The Monty Hall dilemma 6.2 The test paradox 6.3 Problems PART TWO: ESSENTIALS OF PROBABILITY 7 Foundations of probability theory 7.1 Probabilistic foundations 7.2 Compound chance experiments 7.3 Some basic rules 8 Conditional probability and Bayes 8.1 Conditional probability 8.2 Bayes' rule in odds form 8.3 Bayesian statistics 9 Basic rules for discrete random variables 9.1 Random variables 103 104 108 125 134 141 143 151 159 160 164 166 170 177 191 196 197 200 206 207 212 217 221 223 223 231 235 243 243 251 256 263 263 9.2 Expected value 9.3 Expected value of sums of random variables 9.4 Substitution rule and variance 9.5 Independence of random variables 9.6 Special discrete distributions 10 Continuous random variables 10.1 Concept of probability density 10.2 Important probability densities 10.3 Transformation of random variables 10.4 Failure rate function 11 Jointly distributed random variables 11.1 Joint probability densities 11.2 Marginal probability densities 11.3 Transformation of random variables 11.4 Covariance and correlation coefficient 12 Multivariate normal distribution 12.1 Bivariate normal distribution 12.2 Multivariate normal distribution 12.3 Multidimensional central limit theorem 12.4 The chi-square test 13 Conditional distributions 13.1 Conditional probability densities 13.2 Law of conditional probabilities 13.3 Law of conditional expectations 14 Generating functions 14.1 Generating functions 14.2 Moment-generating functions 15 Markov chains 15.1 Markov model 15.2 Transient analysis of Markov chains 15.3 Absorbing Markov chains 15.4 Long-run analysis of Markov chains Appendix Counting methods and ex Recommended reading Answers to odd-numbered problems Bibliography Index 264 268 270 275 279 284 285 296 308 310 313 313 319 323 327 331 331 339 342 348 352 352 356 361 367 367 374 385 386 394 398 404 415 421 422 437 439

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