《随机数学及其应用》涉及随机事件、概率公理、全概率公式、贝叶斯公式、随机变量及其分布、二维变量的联合分布、数学期望、条件期望、大数定律、数理统计等内容。《随机数学及其应用》提供了处理截尾变量均值与方差的半参数界的方法。本书可为广大读者在概率论、高斯过程、小值概率、Stein方法、矩问题等领域进一步学习提供必要的知识储备。
《随机数学及其应用》可作为高等院校英才班本科生双语教材，也可供相关专业研究生、广大教师参考使用。
Chapter 1 Events and Probability
1.1 Events as Sets
1.2 Probability
1.3 Exercises
Chapter 2 Random Variables and Their Distributions
2.1 Random Variables
2.2 Discrete Random Variables
2.3 Expected Value of Discrete Random Variable
2.4 Expectation of a Function of a Discrete Random Variable
2.5 Variance of Random Variables
2.6 Continuous Random Variables
2.7 Distribution of a Function of a Random Variable
2.8 Exercises
Chapter 3 Joint Distributions of Two Random Variables
3.1 Joint Cumulative Probability Distribution Function
3.2 Joint Probability Mass Function for Discrete Random Variable ...
3.3 Joint Probability Density Function
3.4 Independent Random Variables
3.5 Covariance
3.6 Correlation Coefficient
3.7 Bivariate Normal Distribution
3.8 Conditional Distributions
3.9 Joint Probability Distribution of Functions of Random Variables
3.10 Exercises
Chapter 4 Law of Large Numbers
4.1 Generating Functions and Their Applications
4.2 Characteristic Functions
4.3 Limit Theorems
4.4 Law of Large Numbers （LLN）
4.5 Exercises
Chapter 5 Mathematical Statistics
5.1 Introduction
5.2 Random Sampling
5.3 Distributions of Statistics
5.4 The Sample Mean and the Sample Variance
5.5 Point Estimation
5.6 Confidence Intervals
5.7 Testing of Hypotheses
5.8 Exercises
Chapter 6 Approaches to Semiparametric Bounds on Means and Variances
6.1 Introduction to Moment Problems
6.2 Convex Optimization Approach（Duality Theory）
6.3 Semidefinite Programming（SDP）
6.4 Khinchin Transform Method for Unimodal Distributions
6.5 Convex Representation
6.6 Symmetrization Methods for Variance
6.7 Optimal Distance and Optimal Ratio
6.8 Other Methods
Index
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