初等概率论(第4版)(英文版)

本书是一部介绍概率论 及其应用的入门教程。其 原始版本面世已经有30余 年，但仍然是本科一二年 级的经典概率教程。在第4 版中增加了两章讲述应用 和数学金融。传承前面版 本详细、严谨的风格，讲 述了有价证券和期货理论 的基本知识。

PREFACE TO THE FOURTH EDITION PROLOGUE TO INTRODUCTION TO MATHEMATICAL FINANCE 1 SET 1.1 Sample sets 1.2 Operations with sets 1.3 Various relations 1.4 Indicator Exercises 2 PROBABILITY 2.1 Examples of probability 2.2 Definition and illustrations 2.3 Deductions from the axioms 2.4 Independent events 2.5 Arithmetical density Exercises 3 COUNTING 3.1 Fundamental rule 3.2 Diverse ways of sampling 3.3 Allocation models; binomial coefficients 3.4 How to solve it Exercises 4 RANDOM VARIABLES 4.1 What is a random variable? 4.2 How do random variables come about? 4.3 Distribution and expectation 4.4 Integer-valued random variables 4.5 Random variables with densities 4.6 General case Exercises APPENDIX 1: BOREL FIELDS AND GENERAL RANDOM VARIABLES 5 CONDITIONING AND INDEPENDENCE 5.1 Examples of conditioning 5.2 Basic formulas 5.3 Sequential sampling 5.4 P61ya's urn scheme 5.5 Independence and relevance 5.6 Genetical models Exercises 6 MEAN, VARIANCE, AND TRANSFORMS 6.1 Basic properties of expectation 6.2 The density case 6.3 Multiplication theorem; variance and covariance 6.4 Multinomial distribution 6.5 Generating function and the like Exercises 7 POISSON AND NORMAL DISTRIBUTIONS 7.1 Models for Poisson distribution 7.2 Poisson process 7.3 From binomial to normal 7.4 Normal distribution