BOOK DESCRIPTION:
Written by two leading statisticians, this applied introduction to the mathematics of probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.
NEW TO THIS EDITION:
- The included CD-ROM contains all of the data sets in a variety of formats for use with most statistical software packages. This disc also includes several applications of Minitab® and Maple™.
- Historical vignettes at the end of each chapter outline the origin of the greatest accomplishments in the field of statistics, adding enrichment to the course.
Content updates
- The first five chapters have been reorganized to cover a standard probability course with more real examples and exercises. These chapters are important for students wishing to pass the first actuarial exam, and cover the necessary material needed for students taking this course at the junior level.
- Chapters 6 and 7 on estimation and tests of statistical hypotheses tie together confidence intervals and tests, including one-sided ones. There are separate chapters on nonparametric methods, Bayesian methods, and Quality Improvement.
- Chapters 4 and 5 include a strong discussion on conditional distributions and functions of random variables, including Jacobians of transformations and the moment-generating technique. Approximations of distributions like the binomial and the Poisson with the normal can be found using the central limit theorem.
- Chapter 8 (Nonparametric Methods) includes most of the standards tests such as those by Wilcoxon and also the use of order statistics in some distribution-free inferences.
- Chapter 9 (Bayesian Methods) explains the use of the "Dutch book" to prove certain probability theorems.
- Chapter 11 (Quality Improvement) stresses how important W. Edwards Deming's ideas are in understanding variation and how they apply to everyday life.
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 2k 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
"Generally, I think the pedagogy is excellent, providing an almost holistic introduction to statistics, both its mathematical and applications sides. Elements of the subject are introduced in increasing layers of complexity, at a rate that is challenging yet measured. Masterfully done. My overall impression of the book is quite favorable and actually I am considering this text for my next cycle of classes. Strengths: excellent use of examples to illustrate concepts; strong exercise selections; the discussions are generally clear, animated, and focused with the main drive of the text in mind. All the necessary topics central to modern statistics are introduced. The level of the text is quite good for an undergraduate introductory course. Many rather difficult ideas are presented simply, but effectively enough to prepare students for later topics and courses. And the text really bares the soul of statistics. The text motivates the theory by keeping it connected to real-world applications." ― David F. Snyder, Texas State University
"Probability and Statistical Inference is a great text to use for a one-year course, where the students are just becoming mathematically prepared. The authors write with great care and clearly develop and motivate the subject. This edition also contains a chapter on Bayesian methods. Chapter 7 is an interesting and modern treatment of the subject―a subject that has included some controversy. Although I am a probabilist, I am certainly pleased to see this treatment in an undergraduate text. Bayesian methods have long needed suitable treatment at the undergraduate level. It provides an up-to-date and complete treatment of mathematics of probability and statistics. This edition also includes many new examples, applications, and exercises. Each of these has improved in an already outstanding text." ― Randall Swift, California State Polytechnic University, Pomona
"This latest version of Hogg and Tanis contains many more realistic data scenarios that rely much less on coin tossing and dice and card examples. Students will likely better understand the material if they can relate to the examples. The authors strike a good balance between readability and rigor. The material is accurately presented and theorems are accurate. I am glad to see section 6.13 'Resampling Methods' induded. The 'bootstrap' has been around now for 20 years but many mathematical statistics books still neglect it or relegate it to the exercises. This is a good indication that the text is up-to-date." ― Paul Joyce, University of Idaho
"This is a good, solid, calculus-based introduction to probability and statistics at the sophomore-junior level. I have used this textbook twice for such a course, and would like to use it again in the future." ― Ching-Yuan Chiang, James Madison University
"The examples in the book are very clear and easy to follow. My students would benefit from this book more than our current textbook." ― Mark Ghamsary, Loma Linda University
