We are pleased with the reception that was given to the first six editions of
Probability and Statistical Inference. The seventh edition is still designed for use in a course having from three to six semester hours of credit. No previous study of probability or statistics is assumed, and a standard course in calculus provides an adequate mathematical background. Certain sections have been starred and they are not needed in subsequent sections. This, however, does not mean that these starred sections are unimportant, and we hope many of you will study them.
We still view this book as the basis of a junior or senior level course in the mathematics of probability and statistics that is taught by many departments of mathematics and/or statistics. In particular, the first five chapters provide a substantial one-semester course in probability and probability distributions. While many statisticians are teaching a course at this level by minimizing probability and concentrating on statistics, we have found that those studying statistics, actuarial science, electrical engineering, economics, finance, genetics, and so on need probability as much as statistics. Thus we choose to place about equal emphasis on these two topics. Chapters 6-10 consist of the second semester of a two-semester sequence as they cover topics in statistics and statistical inference. We have discovered that a fairly good four-semester-hour course can be constructed by an instructor by selecting topics from the first five chapters and Chapters 6 and 8.
We have tried to make the seventh edition more "user friendly"; yet we do want to reinforce certain basic concepts of mathematics, particularly calculus. To help the student with methods of algebra of sets and calculus, we include a Review of Selected Mathematical Techniques in Appendix A. This review includes a method that makes integration by parts easier. Also, we derive the important Rule of 72, which provides an approximation to the number of years necessary for money to double.
ENHANCEMENTS IN THIS EDITION
- There is better and more logical organization, resulting in a major chapter on the normal distribution.
- A new section gives a brief history of probability, indicating how the normal distribution was discovered.
- More real examples and exercises concerning probability were added that will appeal to students of actuarial science, finance, economics, and so on.
- There is a short but excellent Bayesian chapter, including real example and an indication of how Bayesians prove theorems by establishing "Dutch books."
- In the section on bootstrapping there is an explanation of the origin of this word.
- There are examples of Simpson's paradox.
- Some different statistical techniques, including ordered restricted estimates, have been added.
- There is somewhat more emphasis on the importance of sufficient statistics, noting that such statistics, if they exist, are always used in statistical inferences.
- Tests of hypotheses and confidence intervals are tied together.
- An explanation of the Six Sigma program is in the Epilogue.
- The figures are improved with the use of color.
- The CD-ROM includes not only all of the data sets in different formats, but also many more new applications of Minitab and Maple.
- Illustrations of Maple as a computer algebra system are given in the text and on the CD-ROM.
IMPORTANT POINTS IN THIS EDITION
Chapter 1 is a basic chapter on probability after considering how discrete data can arise. This is followed by a chapter on discrete probability distributions. Chapter 3 starts with continuous type data, introducing stem-and-leaf diagrams, order statistics, and box plots and includes many standard continuous distribution. Chapter 4 introduces multivariate distributions, which are considered with more emphasis than in past editions, including mixtures of discrete and continuous types. Chapter 5 is the climax of the first semester as it is devoted to the important normal distribution, including a brief history of probability noting how the normal distribution was discovered. In these first five chapters over 100 new "real" probability examples and exercises are provided so that we are less dependent upon problems involving coins, cards, and dice. In particular, we hope the reader recognizes the importance of conditional distributions, correlation, and the use of distributions that are mixtures of the discrete and continuous cases.
We begin the second semester with a strong chapter (Chapter 6) on estimation which includes in a starred section the importance of sufficient statistics as shown by the theorem of Rao and Blackwell. This is followed by a new short but modern chapter (Chapter 7) on Bayesian estimation. George Woodworth and Kate Cowles made a number of suggestions concerning this new Bayesian chapter; in particular, Woodworth taught us about a "Dutch book" used in many Bayesian proofs. Chapter 8 is an excellent chapter on tests of statistical hypotheses, and the connection between tests and confidence intervals is given explicitly. Chapter 9 provides some theory of statistical tests. Chapter 10 is short, but interesting, as it considers some of the methods used to improve the quality of manufactured products, although it can be applied to the service industries too. The Six Sigma program is considered in the Epilogue.
We recognize the importance of the computer in modern statistics by including supplements that usually involve the use of the computer. Some of these illustrate the use of Minitab for calculating probabilities, analyzing data, and applications in statistical inference such as tests of hypotheses and confidence intervals. The power of a computer algebra system (CAS) for theoretical computations is illustrated using Maple. The importance of simulation is also demonstrated. Some of these illustrations are printed in the text. There are also many new illustrations on the enclosed CD-ROM and you are encouraged to check these out.
While this book is written primarily as a mathematical introduction to probability and statistics, there are a great many examples and exercises concerned with applications. For illustrations, the reader will find applications in the areas of biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports. That is, there are many exercises in the text, some illustrating the mathematics of probability and statistics but a great number are concerned with applications.
Different from most textbooks, we have included a prologue, a centerpiece, and an epilogue. The main emphasis in these is that variation occurs in almost every process, and the study of probability and statistics helps us understand this variability. Accordingly, the study of statistics is extremely useful in many fields of endeavor and can lead students to interesting positions in the future.
FEATURES
Throughout the book, figures and real applications will help the student understand probability and statistics and what they can accomplish. For some exercises, it is assumed that calculators or computers are available; thus the solutions will not always involve "nice" numbers. The data sets for all of the exercises are available on the enclosed CD-ROM. The data are provided in different formats so that they should be accessible to most computer programs. Finally, in the first part of the book concerning probability, there are supplementary comments inserted about statistics and computation.
ANCILLARIES
A Solutions Manual containing worked out solutions to the even-numbered exercises in the text is available to instructors from the publisher. Many of the numerical exercises were solved using Maple. For additional exercises that involve simulations, a separate manual, Probability & Statistics: Explorations with MAPLE, second edition, by Zaven Karian and Elliot Tanis, is available for purchase. Several exercises in that manual also make use of the power of Maple as a computer algebra system.
The CD-ROM contains all of the data sets in various formats. There are also applications of Minitab for drawing figures, calculating probabilities, calculating characteristics of a sample, and statistical inference. One folder contains some supplementary Maple programs that are useful in probability and statistics. It is these programs that were used for constructing the figures in this text and for other applications. Maple was also used to animate some of the figures in the text. All you need is a browser. Simply load in the directory and you can pull up these animations.