初等概率论 英文版PDF电子书下载

1 SET 1

1.1 Sample sets 1

1.2 Operations with sets 3

1.3 Various relations 7

1.4 Indicator 13

Exercises 17

2 PROBABILITY 20

2.1 Examples of probability 20

2.2 Definition and illustrations 24

2.3 Deductions from the axioms 31

2.4 Independent events 35

2.5 Arithmetical density 39

Exercises 42

3 COUNTING 46

3.1 Fundamental rule 46

3.2 Diverse ways of sampling 49

3.3 Allocation models;binomial coefficients 55

3.4 How to solve it 62

Exercises 70

4 RANDOM VARIABLES 74

4.1 What is a random variable? 74

4.2 How do random variables come about? 78

4.3 Distribution and expectation 84

4.4 Integer-valued random variables 90

4.5 Random variables with densities 95

4.6 General case 105

Exercises 109

APPENDIX 1:BOREL FIELDS AND GENERAL RANDOM VARIABLES 115

5 CONDITIONING AND INDEPENDENCE 117

5.1 Examples of conditioning 117

5.2 Basic formulas 122

5.3 Sequential sampling 131

5.4 Pólya's urn scheme 136

5.5 Independence and relevance 141

5.6 Genetical models 152

Exercises 157

6 MEAN,VARIANCE,AND TRANSFORMS 164

6.1 Basic properties of expectation 164

6.2 The density case 169

6.3 Multiplication theorem;variance and covariance 173

6.4 Multinomial distribution 180

6.5 Generating function and the like 187

Exercises 195

7 POISSON AND NORMAL DISTRIBUTIONS 203

7.1 Models for Poisson distribution 203

7.2 Poisson process 211

7.3 From binomial to normal 222

7.4 Normal distribution 229

7.5 Central limit theorem 233

7.6 Law of large numbers 239

Exercises 246

APPENDIX 2:STIRLING'S FORMULA AND DE MOIVRE-LAPLACE'S THEOREM 251

8 FROM RANDOM WALKS TO MARKOV CHAINS 254

8.1 Problems of the wanderer or gambler 254

8.2 Limiting schemes 261

8.3 Transition probabilities 266

8.4 Basic structure of Markov chains 275

8.5 Further developments 284

8.6 Steady state 291

8.7 Winding up(or down?) 303

Exercises 314

APPENDIX 3:MARTINGALE 325

9 MEAN-VARIANCE PRICING MODEL 329

9.1 An investments primer 329

9.2 Asset return and risk 331

9.3 Portfolio allocation 335

9.4 Diversification 336

9.5 Mean-variance optimization 337

9.6 Asset return distributions 346

9.7 Stable probability distributions 348

Exercises 351

APPENDIX 4:PARETO AND STABLE LAWS 355

10 OPTION PRICING THEORY 359

10.1 Options basics 359

10.2 Arbitrage-free pricing:1-period model 366

10.3 Arbitrage-free pricing:N-period model 372

10.4 Fundamental asset pricing theorems 376

Exercises 377

GENERAL REFERENCES 379

ANSWERS TO PROBLEMS 381

VALUES OF THE STANDARD NORMAL DISTRIBUTION FUNCTION 393

INDEX 397