# Brief Course in Mathematical Statistics, A, CourseSmart eTextbook

Published Date: Dec 21, 2007

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## Description

For a one-semester course in Mathematical Statistics.

This innovative new introduction to Mathematical Statistics covers the important concept of estimation at a point much earlier than other texts (Chapter 2). Thought-provoking pedagogical aids help students test their understanding and relate concepts to everyday life. Ideal for courses that offer a little less probability than usual, this book requires one year of calculus as a prerequisite.

CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.

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

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

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

5.    Computer Oriented Techniques

5.1 Computation of Statistics

5.2 Computer Algebra Systems

5.3 Simulation

5.4 Resampling

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