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 variability. Designed for students with a background in calculus, it reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.

We are pleased with the reception that was given to the first six editions ofProbability 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 aReview of Selected Mathematical Techniquesin Appendix A. This review includes a method that makes integration by parts easier. Also, we derive the importantRule 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 andMaple. Illustrations ofMapleas 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, inclu