Probability and Statistical Inference

Robert V. Hogg, Professor Emeritus of Statistics at the University of Iowa since 2001, received his B.A. in mathematics at the University of Illinois and his M.S. and Ph.D. degrees in mathematics, specializing in actuarial sciences and statistics, from the University of Iowa. Known for his gift of humor and his passion for teaching, Hogg has had far-reaching influence in the field of statistics. Throughout his career, Hogg has played a major role in defining statistics as a unique academic field, and he almost literally "wrote the book" on the subject. He has written more than 70 research articles and co-authored four books including  Introduction of Mathematical Statistics, 6th edition, with J. W. McKean and  A.T. Craig, Applied Statistics for Engineers and Physical Scientists 3rd edtion with J. Ledolter and A Brief Course in Mathematical 1st edition with E.A. Tanis. His texts have become classroom standards used by hundreds of thousands of students.   Among the many awards he has received for distinction in teaching, Hogg has been honored at the national level (the Mathematical Association of America Award for Distinguished Teaching), the state level (the Governor's Science Medal for Teaching), and the university level (Collegiate Teaching Award). His important contributions to statistical research have been acknowledged by his election to fellowship standing in the ASA and the Institute of Mathematical Statistics.   Elliot Tanis, Professor Emeritus of mathematics at Hope College, received his M.S. and Ph.D. degrees from the University of Iowa. Tanis is the co-author of A Brief Course in Mathematical Statistics with R. Hogg and Probability and Statistics: Explorations with MAPLE 2nd edition with Z. Karian. He has authored over 30 publications on statistics and is a past chairman and governor of the Michigan MAA, which presented him with both its Distinguished Teaching and Distinguished Service Awards.  He taught at Hope for 35 years and in 1989 received the HOPE Award (Hope's Outstanding Professor Educator) for his excellence in teaching.  In addition to his academic interests, Dr. Tanis is also an avid tennis player and devoted Hope sports fan.   Dale Zimmerman is The Robert V. Hogg Professor in the Department of Statistics and Actuarial Science at the University of Iowa.

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 Variables 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 Variables 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 Coe±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 Variables

5.1 Functions of One Random Variable

5.2 Transformations of Two Random Variables

5.3 Several 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

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 Su±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 Di®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 Tables

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. Tables

C. Answers to Odd-Numbered Exercises

D. Review of Selected Mathematical Techniques

Index