1 PROBABILITY THEORY
1.1 Set Theory
1.2 Basics of Probability Theory
1.3 Conditional Probability and Independence
1.4 Random Variables
1.5 Distribution Functions
1.6 Density and Mass Functions
1.7 Exercises
1.8 Miscellanea
2 TRANSFORMATIONS AND EXPECTATIONS
2.1 Distributions of Functions of a Random Variable
2.2 Expected Values
2.3 Moments and Moment Generating Functions
2.4 Differentiating Under an Integral Sign
2.5 Exercises
2.6 Miscellanea
3 COMMON FAMILIES OF DISTRIBUTIONS
3.1 Introduction
3.2 Discrete Distributions
3.3 Continuous Distributions
3.4 Exponential Families
3.5 Location and Scale Families
3.6 Inequalities and Identities
3.7 Exercises
3.8 Miscellanea
4 MULTIPLE RANDOM VARIABLES
4.1 Joint and Marginal Distributions
4.2 Conditional Distributions and Independence
4.3 Bivariate Transformations
4.4 Hierarchical Models and Mixture Distributions
4.5 Covariance and Correlation
4.6 Multivariate Distributions
4.7 Inequalities
4.8 Exercises
4.9 Miscellanea
5 PROPERTIES OF A RANDOM SAMPLE
5.1 Basic Concepts of Random Samples
5.2 Sums of Random Variables from a Random Sample
5.3 Sampling from the Normal Distribution
5.4 Order Statistics
5.5 Convergence Concepts
5.6 Generating a Random Sample
5.7 Exercises
5.8 Miscellanea
6 PRINCIPLES OF DATA REDUCTION
6.1 Introduction
6.2 The Sufficiency Principle
6.3 The Likelihood Principle
6.4 The Equivariance Principle
6.5 Exercises
6.6 Miscellanea
7 Point Estimation
7.1 Introduction
7.2 Methods of Finding Estimators
7.3 Methods of Evaluating Estimators
7.4 Exercises
7.5 Miscellanea
8 HYPOTHESIS TESTING
8.1 Introduction
8.2 Methods of Finding Tests
8.3 Methods of Evaluating Tests
8.4 Exercises
8.5 Miscellanca
9 INTERVAL ESTIMATION
9.1 Introduction
9.2 Methods of Finding Interval Estimators
9.3 Methods of Evaluating Interval Estimators
9.4 Exercises
9.5 Miscellanea
10 ASYMPTOTIC EVALUATIONS
10.1 Point Estimation
10.2 Robustness
10.3 Hypothesis Testing
10.4 Interval Estimation
10.5 Exercises
106 Miscellanea
11 ANALYSIS OF VARIANCE AND REGRESSION
11.1 Introduction
11.2 Oneway Analysis of Variance
11.3 Simple Linear Regression
11.4 Exercises
11.5 Miscellanea
12 Regression Models
12.1 Introduction
12.2 Regression with Errors in Variables
12.3 Logistic Regression
12.4 Robust Regression
12.5 Exercises
12.6 Miscellanea
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