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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
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