概率论作为数学的一个重要分支，在众多领域发挥着越来越突出的作用。本书是全球高校采用率最高的概率论教材之一，初版于1976年，多年来不断重印修订，是作者几十年教学和研究经验的结晶。

本书叙述清晰、例子丰富，内容的选取不仅适合学生的兴趣，还有助于学生建立概率直觉。第8版与时俱进，增加了很多新的习题和例子，并新增两节内容，分别推导具有均匀分布和几何分布的随机变量和的分布。本书还附有大量的练习，分为习题、理论习题和自检习题三大类，其中自检习题部分还给出全部解答，有利于巩固和自测所学知识。

本书是世界各国高校广泛采用的概率论教材，通过大量的例子讲述了概率论的基础知识，主要内容有组合分析、概率论公理化、条件概率和独立性、离散和连续型随机变量、随机变量的联合分布、期望的性质、极限定理等．本书附有大量的练习，分为习题、理论习题和自检习题三大类，其中自检习题部分还给出全部解答。

本书适用于大专院校数学、统计、工程和相关专业（包括计算科学、生物、社会科学和管理科学）的学生阅读，也可供概率应用工作者参考。

1 Combinatorial Analysis

 1.1 Introduction

 1.2 The Basic Principle of Counting

 1.3 Permutations

 1.4 Combinations

 1.5 Multinomial Coefficients

 1.6 The Number of Integer Solutions of Equations

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

2 Axioms of Probability

 2.1 Introduction

 2.2 Sample Space and Events

 2.3 Axioms of Probability

 2.4 Some Simple Propositions

 2.5 Sample Spaces Having Equally Likely Outcomes

 2.6 Probability as a Continuous Set Function

 2.7 Probability as a Measure of Belief

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

3 Conditional Probability and Independence

 3.1 Introduction

 3.2 Conditional Probabilities

 3.3 Bayes' Formula

 3.4 Independent Events

 3.5 P(.|F) Is a Probability

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

4 Random Variables

 4.1 Random Variables

 4.2 Discrete Random Variables

 4.3 Expected Value

 4.4 Expectation of a Function of a Random Variable

 4.5 Variance

 4.6 The Bernoulli and Binomial Random Variables

4.6.1 Properties of Binomial Random Variables

4.6.2 Computing the Binomial Distribution Function

 4.7 The Poisson Random Variable

4.7.1 Computing the Poisson Distribution Function

 4.8 Other Discrete Probability Distributions

4.8.1 The Geometric Random Variable

4.8.2 The Negative Binomial Random Variable

4.8.3 The Hypergeometric Random Variable

4.8.4 The Zeta (or Zipf) Distribution

 4.9 Properties of the Cumulative Distribution Function

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

5 Continuous Random Variables

 5.1 Introduction

 5.2 Expectation and Variance of Continuous Random Variables

 5.3 The Uniform Random Variable

 5.4 Normal Random Variables

5.4.1 The Normal Approximation to the Binomial Distribution

 5.5 Exponential Random Variables

5.5.1 Hazard Rate Functions

 5.6 Other Continuous Distributions

5.6.1 The Gamma Distribution

5.6.2 The Weibull Distribution

5.6.3 The Cauchy Distribution

5.6.4 The Beta Distribution

 5.7 The Distribution of a Function of a Random Variable

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

6 Jointly Distributed Random Variables

 6.1 Joint Distribution Functions

 6.2 Independent Random Variables

 6.3 Sums of Independent Random Variables

 6.4 Conditional Distributions: Discrete Case

 6.5 Conditional Distributions: Continuous Case

 6.6 Order Statistics

 6.7 Joint Probability Distribution of Functions of Random Variables

 6.8 Exchangeable Random Variables

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

7 Properties of Expectation

 7.1 Introduction

 7.2 Expectation of Sums of Random Variables

7.2.1 Obtaining Bounds from Expectations via the Probabilistic Method

7.2.2 The Maximum-Minimums Identity

 7.3 Moments of the Number of Events that Occur

 7.4 Covariance, Variance of Sums, and Correlations

 7.5 Conditional Expectation

7.5.1 Definitions

7.5.2 Computing Expectations by Conditioning

7.5.3 Computing Probabilities by Conditioning

7.5.4 Conditional Variance

 7.6 Conditional Expectation and Prediction

 7.7 Moment Generating Functions

7.7.1 Joint Moment Generating Functions

 7.8 Additional Properties of Normal Random Variables

7.8.1 The Multivariate Normal Distribution

7.8.2 The Joint Distribution of the Sample Mean and Sample Variance

 7.9 General Definition of Expectation

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

8 Limit Theorems

 8.1 Introduction

 8.2 Chebyshev's Inequality and the Weak Law of Large Numbers

 8.3 The Central Limit Theorem

 8.4 The Strong Law of Large Numbers

 8.5 Other Inequalities

 8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable

Summary

Problems

Theoretical Exercises

Self-Test Problems and Exercises

9 Additional Topics in Probability

 9.1 The Poisson Process

 9.2 Markov Chains

 9.3 Surprise, Uncertainty, and Entropy

 9.4 Coding Theory and Entropy

Summary

Problems and Theoretical Exercises

Self-Test Problems and Exercises

References

10 Simulation

 10.1 Introduction

 10.2 General Techniques for Simulating Continuous Random Variables

10.2.1 The Inverse Transformation Method

10.2.2 The Rejection Method

 10.3 Simulating from Discrete Distributions

 10.4 Variance Reduction Techniques

10.4.1 Use of Antithetic Variables

10.4.2 Variance Reduction by Conditioning

10.4.3 Control Variates

Summary

Problems

Self-Test Problems and Exercises

Reference

Answers to Selected Problems

Solutions to Self-Test Problems and Exercises

Index