Chapter 1

# Chapter 1 - Lecture Notes on Probability and Statistics...

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Lecture Notes on Probability and Statistics Theory for Economists Yongmiao Hong Department of Statistical Science Cornell University Email: [email protected] January 2011 c 2011 Yongmiao Hong. All rights reserved. 1

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Outline of Contents Chapter 1 Introduction to Econometrics Chapter 2 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 Independence of Events 2.8 Conclusion Chapter 3 Random Variables and Univariate Probability Distributions 3.1 Random Variables and Distribution Functions 3.2 Discrete Random Variable 3.3 Continuous Random Variables 3.4 Functions of a Random Variable 3.5 Mathematical Expectations 3.6 Moment Generating Function 3.7 Characteristic Function Chapter 4 Important Parametric Distributions 4.1 Introduction 4.2 Discrete Distributions 4.3 Continuous Probability Distributions Chapter 5 Random Vectors and Multivariate Probability Distribution 5.1 Random vectors and Joint Probability Distributions 5.2 Marginal Distributions 5.3 Conditional Distributions 5.4 Independence 5.5 Empirical Applications 5.6 Bivariate Transformation 5.7 Expectations Under Multivariate Distributions 2
5.8 Implications of Independence 5.9 Conditional Expectations Chapter 6 Introduction to Sampling Theory and Statistics 6.1 Population and Random Sample 6.2 The Sampling Distribution of the Sample Mean 6.3 The Sampling Distribution of the Sample Variance t Distribution F Distribution 6.6 Su¢ cient Statistics Chapter 7 Convergence Concepts and Limit Theories 7.1 Limits and Orders of Magnitude: A Review 7.2 Motivation for Convergence Concepts 7.3 Convergence in Quadratic Mean and L p -convergence 7.4 Convergence in Probability 7.5 Almost Sure Convergence 7.6 Convergence in Distribution 7.7 Central limit therom and delta method Chapter 8 Parameter Estimation and Evaluation 8.1 Population and Distribution Model 8.2 Maximum Likelihood Estimation 8.3 Method of Moments and Generalized Method of Moments 8.4 Mean Squared Error Criterion 8.5 Best Unbiased Estimators Chapter 9 Hypothesis Testing 9.1 Introduction to Hypothesis Testing 9.2 The Wald Test 9.3 The Lagrangian Multiplier Test 9.4 The Likelihood Ratio Test 9.5 A Simple Example Chapter 10 Conclusion 10.1 Summary 10.2 What next? 3

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Preface to probability theory and statistics. Why do we need to teach probability and statistics to graduate students in economics? Put students for their courses in econometrics, microeconomics, and macroeconomics. Statistics and mathematics are two basic analytic tools in economics. Statistics is an essential tool to study situations involving uncertainties, in the same way as calculus is essential to characterize
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## This note was uploaded on 01/07/2012 for the course ECON 6190 taught by Professor Hong during the Fall '07 term at Cornell.

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Chapter 1 - Lecture Notes on Probability and Statistics...

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