## Table of Contents

Preface

Prologue

**1. Probability**

1.1 Basic Concepts

1.2 Properties of Probability

1.3 Methods of Enumeration

1.4 Conditional Probability

1.5 Independent Events

1.6 Bayes's Theorem

**2. Discrete Distributions**

2.1 Random Variables of the Discrete Type

2.2 Mathematical Expectation

2.3 The Mean, Variance, and Standard Deviation

2.4 Bernoulli Trials and the Binomial Distribution

2.5 The Moment-Generating Function

2.6 The Poisson Distribution

**3. Continuous Distributions**

3.1 Continuous-Type Data

3.2 Exploratory Data Analysis

3.3 Random Variables of the Continuous Type

3.4 The Uniform and Exponential Distributions

3.5 The Gamma and Chi-Square Distributions

3.6 The Normal Distribution

3.7 Additional Models

**4. Bivariate Distributions**

4.1 Distributions of Two Random Variables

4.2 The Correlation Coefficient

4.3 Conditional Distributions

4.4 The Bivariate Normal Distribution

**5. Distributions of Functions of Random Variables**

5.1 Functions of One Random Variable

5.2 Transformations of Two Random Variables

5.3 Several Independent Random Variables

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

**6. Estimation**

6.1 Point Estimation

6.2 Confidence Intervals for Means

6.3 Confidence Intervals for Difference of Two Means

6.4 Confidence Intervals for Variances

6.5 Confidence Intervals for Proportions

6.6 Sample Size.

6.7 A Simple Regression Problem

6.8 More Regression

**7. Tests of Statistical Hypotheses**

7.1 Tests about Proportions

7.2 Tests about One Mean

7.3 Tests of the Equality of Two Means

7.4 Tests for Variances

7.5 One-Factor Analysis of Variance

7.6 Two-Factor Analysis of Variance

7.7 Tests Concerning Regression and Correlation

**8. Nonparametric Methods**

8.1 Chi-Square Goodness of Fit Tests

8.2 Contingency Tables

8.3 Order Statistics

8.4 Distribution-Free Confidence Intervals for Percentiles

8.5 The Wilcoxon Tests

8.6 Run Test and Test for Randomness

8.7 Kolmogorov-Smirnov Goodness of Fit Test

8.8 Resampling Methods

**9. Bayesian Methods**

9.1 Subjective Probability

9.2 Bayesian Estimation

9.3 More Bayesian Concepts

**10. Some Theory**

10.1 Sufficient Statistics

10.2 Power of a Statistical Test

10.3 Best Critical Regions

10.4 Likelihood Ratio Tests

10.5 Chebyshev's Inequality and Convergence in Probability

10.6 Limiting Moment-Generating Functions

10.7 Asymptotic Distributions of Maximum Likelihood Estimators

**11. Quality Improvement Through Statistical Methods**

11.1 Time Sequences

11.2 Statistical Quality Control

11.3 General Factorial and 2^{k }Factorial Designs

11.4 Understanding Variation

A. Review of Selected Mathematical Techniques

A.1 Algebra of Sets

A.2 Mathematical Tools for the Hypergeometric Distribution

A.3 Limits

A.4 Infinite Series

A.5 Integration

A.6 Multivariate Calculus

B. References

C. Tables

D. Answers to Odd-Numbered Exercises