Table of Contents
Preface
1. Introduction
1.1 What Is Probability?
1.2 What Is Statistics?
2. Probability
2.1 Introduction
2.2 Axioms of Probability
2.3 Counting Techniques
2.4 Conditional Probability and Independence
2.5 Probability Calculations
Exercises
3. Random Variables And Probability Distributions
3.1 Definitions of a Random Variable
3.2 Discrete Random Variables
3.3 Univariate Continuous Random Variables
3.4 Bivariate Continuous Random Variables
3.5 Distribution Function
3.6 Change of Variables
3.7 Joint Distribution of Discrete and Continuous Random Variables
Exercises
4. Moments
4.1 Expected Value
4.2 Higher Moments
4.3 Covariance and Correlation
4.4 Conditional Mean and Variance
Exercises
5. Binomial And Normal Random Variables
5.1 Binomial Random Variables
5.2 Normal Random Variables
5.3 Bivariate Normal Random Variables
5.4 Multivariate Normal Random Variables
Exercises
6. Large Sample Theory
6.1 Modes of Convergence
6.2 Laws of Large Numbers and Central Limit Theorems
6.3 Normal Approximation of Binomial
6.4 Examples
Exercises
7. Point Estimation
7.1 What Is an Estimator?
7.2 Properties of Estimators
7.3 Maximum Likelihood Estimator: Definition and Computation
7.4 Maximum Likelihood Estimator: Properties
Exercises
8. Interval Estimation
8.1 Introduction
8.2 Confidence Intervals
8.3 Bayesian Method
Exercises
9. Tests Of Hypotheses
9.1 Introduction
9.2 Type I and Type II Errors
9.3 Neyman-Pearson Lemma
9.4 Simple against Composite
9.5 Composite against Composite
9.6 Examples of Hypothesis Tests
9.7 Testing about a Vector Parameter
Exercises
10. Bivariate Regression Model
10.1 Introduction
10.2 Least Squares Estimators
10.3 Tests of Hypotheses
Exercises
11. Elements Of Matrix Analysis
11.1 Definition of Basic Terms
11.2 Matrix Operations
11.3 Determinants and Inverses
11.4 Simultaneous Linear Equations
11.5 Properties of the Symmetric Matrix
Exercises
12. Multiple Regression Model
12.1 Introduction
12.2 Least Squares Estimators
12.3 Constrained Least Squares Estimators
12.4 Tests of Hypotheses
12.5 Selection of Regressors
Exercises
13. Econometric Models
13.1
