Probability

양장본 Hardcover

Robert P Dobrow 저자(글)

John Wiley & Sons (Asia) Pte. · 2014년 04월 30일

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작가정보

저자(글) Robert P Dobrow

목차

• Preface xiAcknowledgments xivIntroduction xv1 First Principles 11.1 Random Experiment, Sample Space, Event 11.2 What Is a Probability? 31.3 Probability Function 41.4 Properties of Probabilities 71.5 Equally Likely Outcomes 101.6 Counting I 121.7 Problem-Solving Strategies: Complements, Inclusion-Exclusion 141.8 Random Variables 181.9 A Closer Look at Random Variables 211.10 A First Look at Simulation 221.11 Summary 26Exercises 272 Conditional Probability 342.1 Conditional Probability 342.2 New Information Changes the Sample Space 392.3 Finding P(A and B) 402.4 Conditioning and the Law of Total Probability 492.5 Bayes Formula and Inverting a Conditional Probability 572.6 Summary 61Exercises 623 Independence and Independent Trials 683.1 Independence and Dependence 683.2 Independent Random Variables 763.3 Bernoulli Sequences 773.4 Counting II 793.5 Binomial Distribution 883.6 Stirling's Approximation 953.7 Poisson Distribution 963.8 Product Spaces 1053.9 Summary 107Exercises 1094 Random Variables 1174.1 Expectation 1184.2 Functions of Random Variables 1214.3 Joint Distributions 1254.4 Independent Random Variables 1304.5 Linearity of Expectation 1354.6 Variance and Standard Deviation 1404.7 Covariance and Correlation 1494.8 Conditional Distribution 1564.9 Properties of Covariance and Correlation 1624.10 Expectation of a Function of a Random Variable 1644.11 Summary 165Exercises 1685 A Bounty of Discrete Distributions 1765.1 Geometric Distribution 1765.2 Negative Binomial--Up from the Geometric 1845.3 Hypergeometric--Sampling Without Replacement 1895.4 From Binomial to Multinomial 1945.5 Benford's Law 2015.6 Summary 203Exercises 2056 Continuous Probability 2116.1 Probability Density Function 2136.2 Cumulative Distribution Function 2166.3 Uniform Distribution 2206.4 Expectation and Variance 2226.5 Exponential Distribution 2246.6 Functions of Random Variables I 2296.7 Joint Distributions 2356.8 Independence 2436.9 Covariance, Correlation 2496.10 Functions of Random Variables II 2516.11 Geometric Probability 2566.12 Summary 262Exercises 2657 Continuous Distributions 2737.1 Normal Distribution 2737.2 Gamma Distribution 2907.3 Poisson Process 2967.4 Beta Distribution 3047.5 Pareto Distribution, Power Laws, and the 80-20 Rule 3087.6 Summary 312Exercises 3158 Conditional Distribution, Expectation, and Variance 3228.1 Conditional Distributions 3228.2 Discrete and Continuous: Mixing it up 3288.3 Conditional Expectation 3328.4 Computing Probabilities by Conditioning 3428.5 Conditional Variance 3468.6 Summary 352Exercises 3539 Limits 3599.1 Weak Law of Large Numbers 3619.2 Strong Law of Large Numbers 3679.3 Monte Carlo Integration 3729.4 Central Limit Theorem 3769.5 Moment-Generating Functions 3859.6 Summary 391Exercises 39210 Additional Topics 39910.1 Bivariate Normal Distribution 39910.2 Transformations of Two Random Variables 40710.3 Method of Moments 41110.4 Random Walk on Graphs 41310.5 Random Walks on Weighted Graphs and Markov Chains 42110.6 From Markov Chain to Markov Chain Monte Carlo 42910.7 Summary 440Exercises 442Appendix A Getting Started with R 447Appendix B Probability Distributions in R 458Appendix C Summary of Probability Distributions 459Appendix D Reminders from Algebra and Calculus 462Appendix E More Problems for Practice 464Solutions to Exercises 469References 487Index 491

기본정보

ISBN	9781118241257 ( 1118241258 )
발행(출시)일자	2014년 04월 30일
쪽수	520쪽
크기	152 * 236 * 30 mm / 816 g
총권수	1권
언어	영어