概率论入门(英文版)
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作者(美)雷斯尼克|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787510058271
出版时间2013-03
装帧其他
开本其他
定价89元
货号30968497
上书时间2024-06-13
商品详情
- 品相描述：全新
- 商品描述
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目录
Preface
1 Sets and Events
1.1 Introduction
1.2 Basic Set Theory
1.2.1 Indicator functions
1.3 Limits of Sets
1.4 Monotone Sequences
1.5 Set Operations and Closure
1.5.1 Examples
1.6 The σ-field Generated by a Given Class C
1.7 Borel Sets on the Real Line
1.8 Comparing Borel Sets
1.9 Exercises
2 Probability Spaces
2.1 Basic Definitions and Properties
2.2 More on Closure
2.2.1 Dynkin's theorem
2.2.2 Proof of Dynkin's theorem
2.3 Two Constructions
2.4 Constructions of Probability Spaces
2.4.1 General Construction of a Probability Model
2.4.2 Proof of the Second Extension Theorem
2.5 Measure Constructions
2.5.1 Lebesgue Measure on (0,1]
2.5.2 Construction of a Probability Measure on R with Given Distribution Function F(x)
2.6 Exercises
3 Random Variables,Elements,and Measurable Maps
3.1 Inverse Maps
3.2 Measurable Maps,Random Elements, Induced Probability Measures
3.2.1 Composition
3.2.2 Random Elements of Metric Spaces
3.2.3 Measurability and Continuity
3.2.4 Measurability and Limits
3.3 σ-Fields Generated by Maps
3.4 Exercises
4 Independence
4.1 Basic Definitions
4.2 Independent Random Variables
4.3 Two Examples of Independence
4.3.1 Records,Ranks,Renyi Theorem
4.3.2 Dyadic Expansions of Uniform Random Numbers
4.4 More on Independence:Groupings
4.5 Independence,Zero-One Laws,Borel-Cantelli Lemma
4.5.1 Borel-Cantelli Lemma
4.5.2 Borel Zero-One Law
4.5.3 Kolmogorov Zero-One Law
4.6 Exercises
5 Integration and Expectation
5.1 Preparation for Integration
5.1.1 Simple Functions
内容摘要
本书是一部十分经典的概率论教程。1999年初版，2001年第2次重印，2003年第3次重印，同年第4次重印，2005年第5次重印，受欢迎程度可见一斑。大多数概率论书籍是写给数学家看的，漂亮的数学材料是吸引读者的一大亮点；相反地，本书目标读者是数学及非数学专业的研究生，帮助那些在统计、应用概率论、生物、运筹学、数学金融和工程研究中需要深入了解高等概
率论的所有人员。
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