Brief Course in Mathematical Statistics, A

Preface

1.    Probability

    1.1 Basic Concepts

    1.2 Methods of Enumeration

    1.3 Conditional Probability

    1.4 Independent Events

    1.5 Bayes's Theorem

Chapter One Comments

2.    Discrete Distributions

    2.1 Discrete Probability Distributions

    2.2 Expectations

    2.3 Special Discrete Distributions

    2.4 Estimation

    2.5 Linear Functions of Independent Random Variables

    2.6 Multivariate Discrete Distributions

Chapter Two Comments

3.    Continuous Distributions

    3.1 Descriptive Statistics and EDA

    3.2 Continuous Probability Distributions

    3.3 Special Continuous Distributions

    3.4 The Normal Distribution

    3.5 Estimation in the Continuous Case

    3.6 The Central Limit Theorem

    3.7 Approximations for Discrete Distributions

Chapter Three Comemnts

4.    Applications of Statistical Inference

    4.1 Summary of Necessary Theoretical Results

    4.2 Confidence Intervals Using _X² F,and T

    4.3 Confidence Intervals and Tests of Hypotheses

    4.4 Basic Tests Concerning One Parameter

    4.5 Tests of the Equality of Two Parameters

    4.6 Simple Linear Regression

    4.7 More on Linear Regression

    4.8 One-Factor Analysis of Variance

    4.9 Distribution-Free Confidence and Tolerance Intervals

    4.10 Chi-Square Goodness of Fit Tests

    4.11 Contingency Tables

Chapter Four Comments

5.    Computer Oriented Techniques

    5.1 Computation of Statistics

    5.2 Computer Algebra Systems

    5.3 Simulation

    5.4 Resampling

Chapter Five Comments

6.    Some Sampling Distribution Theory

    6.1 Moment-Generation Function Technique

    6.2 M.G.F of Linear Functions

    6.3 Limiting Moment-Generating Functions

    6.4 Use of Order Statistics in Non-regular Cases

Chapter Six Comments