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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