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- 引言
- 1.1 General methodology of modern
- 1.2 Roles of Econometrics
- 1.3 Illustrative Examples
- 1.4 Roles of Probability and Statistics
- 2.0 Foundation of Probability Theory
- 2.1 Random Experiments
- 2.2 Basic Concepts of Probability
- 2.3 Review of Set Theory
- 2.4 Fundamental Probability Laws
- 2.5 Methods of Counting
- 2.6 Conditional Probability
- 2.7 Bayes' Theorem
- 2.8 Independence
- 2.9 Conclusion
- 3.0 Random Variables and Univariate Probability Distributions
- 3.1 Random Variables
- 3.2 Cumulative Distribution Function
- 3.3 Discrete Random Variables(DRV)
- 3.4 Continuous Random Variables
- 3.5 Functions of a Random Variable
- 3.6 Mathematical Expectations
- 3.7 Moments
- 3.8 Quantiles
- 3.9 Moment Generating Function (MGF)
- 3.10 Characteristic
- 3.11 Conclusion
- 4.1 Important Probability Distributions
- 4.2 Discrete Probability Distributions
- 4.3 Continuous Probability Distributions
- 4.4 Conclusion
- 5.0 Multivariate Probability Distributions
- 5.1 Random Vectors and Joint Probability Distributions
- 5.2 Marginal Distributions
- 5.3 Conditional Distributions
- 5.4 Independence
- 5.5 Bivariate Transformation
- 5.6 Bivariate Normal Distribution
- 5.7 Expectations and Covariance
- 5.8 Joint Moment Generating Function
- 5.9 Implications of Independence on Expectations
- 5.10 Conditional Expectations
- 5.11 Conclusion
- 上期复习与本期导学
- 6.0 Introduction to Statistic
- 6.1 Population and Random Sample
- 6.2 Sampling Distribution of Sample Mean
- 6.3 Sampling Distribution of Sample Variance
- 6.4 Student’s t-Distribution
- 6.5 Snedecor's F Distribution
- 6.6 Sufficient Statistics
- 6.7 Conclusion
- 7.0 Convergences and Limit Theorems
- 7.1 Limits and Orders of Magnitude-A Review
- 7.2 Motivation for Convergence Concepts
- 7.3 Convergence in Quadratic Mean and Lp-Convergence
- 7.4 Convergence in Probability
- 7.5 Almost Sure Convergence
- 7.6 Convergence in Distribution
- 7.7 Central Limit Theorems_batch
- 8.1 Population and Distribution Model
- 8.2 Maximum Likelihood Estimation
- 8.3 Asymptotic Properties of MLE
- 8.4 Method of Moments and Generalized Method of Moments
- 8.5 Asymptotic Properties of GMM
- 8.6 Mean Squared Error Criterion
- 8.7 Best Unbiased Estimators
- 8.8 Cramer-Rao Lower Bound
- 9.1 Introduction to Hypothesis Testing
- 9.2 Neyman-Pearson Lemma
- 9.3 Wald Test
- 9.4 Lagrangian Multiplier (LM) Test
- 9.5 Likelihood Ratio Test
- 9.6 Illustrative Examples
- 10.1 Big Data, Machine Learning and Statistics
- 10.2 Empirical Studies and Statistical Inference
- 10.3 Important Features of Big Data
- 10.4 Big Data Analysis and Statistics
- 讲座:概率论与统计学在经济学中的应用
概率论与数理统计的相关介绍
洪永淼教授的 《概率论与统计学》课程可供经济学、金融学、管理学、统计学、应用数学、数据科学等相关专业的研究生和高年级本科生学习。 课程使用教材为洪永淼教授的英文版专著《Probability and Statistics for Economists》( Yongmiao Hong, World Scientific, 2017)以及中文版教材《概率论与统计学》(洪永淼,中国统计出版社,2017)。课程网站(课件地址)(https://probability.xmu.edu.cn/)。
概率论与数理统计课程是大学数学公共基础课程之一,是一门应用性很强的学科。各种工程问题和社会、经济问题都与之相关,如工程可靠性度量、金融风险、保险精算、环境保护、可持续发展等领域需要运用概率统计知识。它是继高等数学、线性代数之后,理、工、经管、生医类所有专业必需的公共基础课程,对培养学生处理“随机”的数学基础知识、基本能力和综合素质具有其他课程不能替代的作用,对实现各类专业培养研究型、探索型、创新型人才提供了科学研究和基础实践的平台。