| Sheldon M.Ross国际知名概率与统计学家，南加州大学工业工程与运筹系系主任。毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。研究领域包括：随机模型．仿真模拟、统计分析、金融数学等：Ross教授著述颇丰，他的多种畅销数学和统计教材均产生了世界性的影响，如Introduction to Probability Models(《应用随机过程：概率模型导论》)，A First Course in Probability(《概率论墓础教程》)等(均由人民邮电出版社出版)。 |
| 1.Introduction to Probability Theory 1.1.Introduction 1.2.Sample Space and Events 1.3.Probabilities Defined on Events 1.4.Conditional Probabilities 1.5.Independent Events 1.6.Bayes' Formula Exercises References 2.Random Variables 2.1.Random Variables 2.2.Discrete Random Variables 2.3.Continuous Random Variables 2.4.Expectation of a Random Variable 2.5.Jointly Distributed Random Variables 2.6.Moment Generating Functions 2.7.Limit Theorems 2.8.Stochastic Processes Exercises References 3.Conditional Probability and Conditional Expectation 3.1.Introduction 3.2.The Discrete Case 3.3.The Continuous Case 3.4.Computing Expectations by Conditioning 3.5.Computing Probabilities by Conditioning 3.6.Some Applications 3.7.An Identity for Compound Random Variables Exercises 4.Markov Chains 4.1.Introduction 4.2.Chapman-Kolmogorov Equations 4.3.Classification of States 4.4.Limiting Probabilities 4.5.Some Applications 4.6.Mean Time Spent in Transient States 4.7.Branching Processes 4.8.Time Reversible Markov Chains 4.9.Markov Chain Monte Carlo Methods 4.10.Markov Decision Processes 4.11.Hidden Markov Chains Exercises References 5.The Exponential Distribution and the Poisson Process 5.1.Introduction 5.2.The Exponential Distribution 5.3.The Poisson Process 5.4.Generalizations of the Poisson Process Exercises References 6.Continuous-Time Markov Chains 7.Renewal Theory and Its Applications 8.Queueing Theory 9.Reliability Theory 10.Brownian Motion and Stationary Processes 11.Simulation Appendix: Solutions to Starred Exercises Index |
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