《隨機數學及其應用》涉及隨機事件、概率公理、全概率公式、貝葉斯公式、隨機變量及其分布、二維變量的聯(lián)合分布、數學期望、條件期望、大數定律、數理統(tǒng)計等內容�！峨S機數學及其應用》提供了處理截尾變量均值與方差的半參數界的方法。本書可為廣大讀者在概率論、高斯過程、小值概率、Stein方法、矩問題等領域進一步學習提供必要的知識儲備。
《隨機數學及其應用》可作為高等院校英才班本科生雙語教材，也可供相關專業(yè)研究生、廣大教師參考使用。
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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