概率论与数理统计

Chapter 1 Probability

1.1 Introduction

1.2 Sample Space and Events

1.3 Axioms of Probability

1.4 Some Simple Propositions

1.5 Sample Spaces Having Equally Likely Outcomes

1.6 Conditional Probabilities

1.7 Bayes's Formula

1.8 Independent Events

Exercise 1

Chapter 2 Discrete Random Variables and Probability Distributions

2.1 Random Variables

2.2 Probability Distributions for Discrete Random Variables

2.3 The Binomial and Poisson Probability Distributions

Exercise 2

Chapter 3 Continuous Random Variables and Probability Distributions

3.1 Probability Density Functions

3.2 Cumulative Distribution Functions

3.3 The Normal Distributions

3.4 The Exponential and Gamma Distributions

3.5 Other Continuous Distributions

Exercise 3

Chapter 4 Joint Probability Distributions

4.1 Joint Distribution Functions

4.2 Marginal Distribution Functions

4.3 Conditional Distributions

4.4 Independent Random Variables

4.5 Sums of Independent Random Variables

4.6 Joint Probability Distribution of Function of Random Variables

Exercise 4

Chapter 5 Mathematical Expectation

5.1 Expectation of a Random Variable

5.2 Variance and Variance of sums

5.3 Covariance and Correlations

5.4 Conditional Expectation

5.5 Chebyshev's Theorem

Exercise 5

Chapter 6 Limit Theorems

6.1 The Weak Law of Large Numbers

6.2 The Central Limit Theorem

Exercise 6

Chapter 7 Descriptive Statistics

7.1 Populations and Samples

7.2 Measures of Center and Variability

7.3 Sampling Distributions

7.4 Chi-squared Distribution，t-Distribution and F-Distribution

Exercise 7

Chapter 8 Estimation

8.1 Point Estimation

8.2 The Particular Properties of Estimators

8.3 Interval Estimation

Exercise 8

Appendix

Reference

《概率论与数理统计（英文版）》共8章，主要内容包括随机事件和概率、随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、数理统计的基本知识、参数估计、假设检验、方差分析。