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初等概率论 英文版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

初等概率论 英文版
  • KaiLaiChung著 著
  • 出版社： 世界图书北京出版公司
  • ISBN：9787510004629
  • 出版时间：2010
  • 标注页数：404页
  • 文件大小：14MB
  • 文件页数：414页
  • 主题词：概率论－高等学校－教材－英文

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图书目录

1 SET1

1.1 Sample sets1

1.2 Operations with sets3

1.3 Various relations7

1.4 Indicator13

Exercises17

2 PROBABILITY20

2.1 Examples of probability20

2.2 Definition and illustrations24

2.3 Deductions from the axioms31

2.4 Independent events35

2.5 Arithmetical density39

Exercises42

3 COUNTING46

3.1 Fundamental rule46

3.2 Diverse ways of sampling49

3.3 Allocation models;binomial coefficients55

3.4 How to solve it62

Exercises70

4 RANDOM VARIABLES74

4.1 What is a random variable?74

4.2 How do random variables come about?78

4.3 Distribution and expectation84

4.4 Integer-valued random variables90

4.5 Random variables with densities95

4.6 General case105

Exercises109

APPENDIX 1:BOREL FIELDS AND GENERAL RANDOM VARIABLES115

5 CONDITIONING AND INDEPENDENCE117

5.1 Examples of conditioning117

5.2 Basic formulas122

5.3 Sequential sampling131

5.4 Pólya's urn scheme136

5.5 Independence and relevance141

5.6 Genetical models152

Exercises157

6 MEAN,VARIANCE,AND TRANSFORMS164

6.1 Basic properties of expectation164

6.2 The density case169

6.3 Multiplication theorem;variance and covariance173

6.4 Multinomial distribution180

6.5 Generating function and the like187

Exercises195

7 POISSON AND NORMAL DISTRIBUTIONS203

7.1 Models for Poisson distribution203

7.2 Poisson process211

7.3 From binomial to normal222

7.4 Normal distribution229

7.5 Central limit theorem233

7.6 Law of large numbers239

Exercises246

APPENDIX 2:STIRLING'S FORMULA AND DE MOIVRE-LAPLACE'S THEOREM251

8 FROM RANDOM WALKS TO MARKOV CHAINS254

8.1 Problems of the wanderer or gambler254

8.2 Limiting schemes261

8.3 Transition probabilities266

8.4 Basic structure of Markov chains275

8.5 Further developments284

8.6 Steady state291

8.7 Winding up(or down?)303

Exercises314

APPENDIX 3:MARTINGALE325

9 MEAN-VARIANCE PRICING MODEL329

9.1 An investments primer329

9.2 Asset return and risk331

9.3 Portfolio allocation335

9.4 Diversification336

9.5 Mean-variance optimization337

9.6 Asset return distributions346

9.7 Stable probability distributions348

Exercises351

APPENDIX 4:PARETO AND STABLE LAWS355

10 OPTION PRICING THEORY359

10.1 Options basics359

10.2 Arbitrage-free pricing:1-period model366

10.3 Arbitrage-free pricing:N-period model372

10.4 Fundamental asset pricing theorems376

Exercises377

GENERAL REFERENCES379

ANSWERS TO PROBLEMS381

VALUES OF THE STANDARD NORMAL DISTRIBUTION FUNCTION393

INDEX397

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