导语

  

内容提要

  

    本书系浙江大学出版社版的《概率论》教材的配套英文教材，内容主要包括四大部分：一、随机事件及其概率；二、随机变量和分布函数；三、数字特征；四、极限定理。通过学习，使学生掌握概率论的基本概念和主要结果，了解定量地处理随机现象的基本思想，了解它在其它学科和实际部门的广泛应用，也为学习数理统计等后续课程奠定基础。

Chapter 1  Events and Probabilities
  1.1  Random phenomena and statistical regularity
    1.1.1  Random phenomena
    1.1.2  The statistical definition of probability
  1.2  Classical probability models
    1.2.1  Sample points and sample spaces
    1.2.2  Discrete probability models
    1.2.3  Geometric probability models
  1.3  The axiomatic definition of probability
    1.3.1  Events
    1.3.2  Probability space
    1.3.3  Continuity of probability measure
  1.4  Conditional probability and independent events
    1.4.1  Conditional probability
    1.4.2  Total probability formula and Bayes' rule
    1.4.3  Independent events
Chapter 2  Random Variables and Distribution Functions
  2.1  Discrete random variables
    2.1.1  The concept of random variables
    2.1.2  Discrete random variables
  2.2  Distribution functions and continuous random variables
    2.2.1  Distribution functions
    2.2.2  Continuous random variables and density functions
    2.2.3  Typical continuous random variables
  2.3  Random vectors
    2.3.1  Discrete random vectors
    2.3.2  Joint distribution functions
    2.3.3  Continuous random vectors
  2.4  Independence of random variables
  2.5  Conditional distribution
    2.5.1  Discrete case
    2.5.2  Continuous case
    2.5.3  The general case
    2.5.4  The conditional probability given a random variable
  2.6  Functions of random variables
    2.6.1  Functions of discrete random variables
    2.6.2  Functions of continuous random variables
    2.6.3  Functions of continuous random vectors
    2.6.4  Transforms of random vectors
    2.6.5  Important distributions in statistics
Chapter 3  Numerical Characteristics and Characteristic Functions
  3.1  Mathematical expectations
    3.1.1  Expectations of discrete random variables
    3.1.2  Expectations of continuous random variables
    3.1.3  General definition
    3.1.4  Expectations of functions of random variables
    3.1.5  Basic properties of expectations
    3.1.6  Conditional expectation
  3.2  Variances, covariances and correlation coefficients
    3.2.1  Variances
    3.2.2  Covariances
    3.2.3  Correlation coefficients
    3.2.4  Moments
  3.3  Characteristic functions
    3.3.1  Definitions
    3.3.2  Properties
    3.3.3  Inverse formula and uniqueness theorem
    3.3.4  Additivity of distribution functions
    3.3.5  Multivariate characteristic functions
  3.4  Multivariate normal distributions
    3.4.1  Density functions and characteristic functions
    3.4.2  Properties
Chapter 4  Probability Limit Theorems
  4.1  Convergence in distribution and central limit theorems  ...
    4.1.1  Weak convergence of distribution functions
    4.1.2  Central limit theorems
  4.2  Convergence in probability and weak law of large numbers
    4.2.1  Convergence in probability
    4.2.2  Weak law of large numbers
  4.3  Almost sure convergence and strong laws of large numbers
    4.3.1  Almost sure convergence
    4.3.2  Strong laws of large numbers
  Bibliography
Appendix A  Distribution of Typical Random Variables
  A.1  Distribution of Typical Random Variables
  A.2  Distributions of Typical Random Variables
Appendix B  Tables
  B.1  Table of Binomial Probabilities
  B.2  Table of Random Digits
  B.3  Table of Poisson Probabilities
  B.4  Table of Standard Normal Distribution Function
  B.5  Table of X2 Distribution
  B.6  Table of t Distribution