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Table of Contents

Preface

Prologue

1. Probability

1.1 Properties of Probability

1.2 Methods of Enumeration

1.3 Conditional Probability

1.4 Independent Events

1.5 Bayes’ Theorem

2. Discrete Distributions

2.1 Random VariTables of the Discrete Type

2.2 Mathematical Expectation

2.3 Special Mathematical Expectations

2.4 The Binomial Distribution

2.5 The Negative Binomial Distribution

2.6 The Poisson Distribution

3. Continuous Distributions

3.1 Random VariTables of the Continuous Type

3.2 The Exponential, Gamma, and Chi-Square Distributions

3.3 The Normal Distribution

3.4 Additional Models

4. Bivariate Distributions

4.1 Bivariate Distributions of the Discrete Type

4.2 The Correlation CoeÂ±cient

4.3 Conditional Distributions

4.4 Bivariate Distributions of the Continuous Type

4.5 The Bivariate Normal Distribution

5. Distributions of Functions of Random VariTables

5.1 Functions of One Random VariTable

5.2 Transformations of Two Random VariTables

5.3 Several Random VariTables

5.4 The Moment-Generating Function Technique

5.5 Random Functions Associated with Normal Distributions

5.6 The Central Limit Theorem

5.7 Approximations for Discrete Distributions

5.8 Chebyshev’s Inequality and Convergence in Probability

5.9 Limiting Moment-Generating Functions

6. Point Estimation

6.1 Descriptive Statistics

6.2 Exploratory Data Analysis

6.3 Order Statistics

6.4 Maximum Likelihood Estimation

6.5 A Simple Regression Problem

6.6 Asymptotic Distributions of Maximum Likelihood Estimators

6.7 SuÂ±cient Statistics

6.8 Bayesian Estimation

6.9 More Bayesian Concepts

7. Interval Estimation

7.1 Confidence Intervals for Means

7.2 Confidence Intervals for the DiÂ®erence of Two Means

7.3 Confidence Intervals for Proportions

7.4 Sample Size

7.5 Distribution-Free Confidence Intervals for Percentiles

7.6 More Regression

7.7 Resampling Methods

8. Tests of Statistical Hypotheses

8.1 Tests about One Mean

8.2 Tests of the Equality of Two Means

8.3 Tests about Proportions

8.4 The Wilcoxon Tests

8.5 Power of a Statistical Test

8.6 Best Critical Regions

8.7 Likelihood Ratio Tests

9. More Tests

9.1 Chi-Square Goodness-of-Fit Tests

9.2 Contingency TTables

9.3 One-Factor Analysis of Variance

9.4 Two-Way Analysis of Variance

9.5 General Factorial and 2k Factorial Designs

9.6 Tests Concerning Regression and Correlation

9.7 Statistical Quality Control

Epilogue

A. References

B. TTables

C. Answers to Odd-Numbered Exercises

D. Review of Selected Mathematical Techniques

Index