本书是全球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，书中附有大量的练习，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。

本书作为概率论的入门书，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。

本书是全球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。

本书作为概率论的入门书，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　

　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　

　Theoretical Exercises　

　Self-Test Problems and Exercises　

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　

APPENDICES

A　Answers to Selected Problems　

B　Solutions to Self-Test Problems and Exercises

Index