Mathematical Statistics
Lecture Notes
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TABLE OF CONTENTS
TABLE of CONTENTS
1 Probability Distribution of Functions Of Random Variables
1.1 Preliminaries
1.2 Distribution of Order Statistics
1.3 Functions of Random Variables
1.4 Convergence and Limit Theorems
1.5 Practice problems: distributions and transformations
1.6 Practice problems: limit theorems
2 Estimation
2.1 Introduction
2.2 Method of Moments
2.3 Method of Least Squares
2.4 Method of Maximum Likelihood
2.5 Properties of Estimators
2.6 Practice problems
3 Hypothesis Testing
3.1 Introduction
3.2 Most Powerful Tests
3.3 Uniformly Most Powerful Tests
3.4 Generalised Likelihood Ratio Tests
3.5 Practice problems
4 Review Problems
4.1 Review Problem 1
4.2 Review Problem 2
4.3 Review Problem 3
4.4 Review Problem 4
4.5 Review Problem 5
4.6 Review Problem 6
TABLE of CONTENTS
1 Probability Distribution of Functions Of Random Variables
1.1 Preliminaries
1.2 Distribution of Order Statistics
1.3 Functions of Random Variables
1.4 Convergence and Limit Theorems
1.5 Practice problems: distributions and transformations
1.6 Practice problems: limit theorems
2 Estimation
2.1 Introduction
2.2 Method of Moments
2.3 Method of Least Squares
2.4 Method of Maximum Likelihood
2.5 Properties of Estimators
2.6 Practice problems
3 Hypothesis Testing
3.1 Introduction
3.2 Most Powerful Tests
3.3 Uniformly Most Powerful Tests
3.4 Generalised Likelihood Ratio Tests
3.5 Practice problems
4 Review Problems
4.1 Review Problem 1
4.2 Review Problem 2
4.3 Review Problem 3
4.4 Review Problem 4
4.5 Review Problem 5
4.6 Review Problem 6