- Text
- Probability,
- Density,
- Variable,
- Variables,
- Interval,
- Variance,
- Population,
- Distributions,
- Hypothesis,
- Theorem,
- Mathematical,
- Statistics,
- Applications,
- Edition,
- Marvin.pcriot.com

www.downloadslide.com PREFACE The Purpose and Prerequisites of this Book **Mathematical** **Statistics** **with** **Applications** was written for use **with** an undergraduate 1-year sequence of courses (9 quarter- or 6 semester-hours) on mathematical statistics. The intent of the text is to present a solid undergraduate foundation in statistical theory while providing an indication of the relevance and importance of the theory in solving practical problems in the real world. We think a course of this type is suitable for most undergraduate disciplines, including mathematics, where contact **with** applications may provide a refreshing and motivating experience. The only mathematical prerequisite is a thorough knowledge of first-year college calculus— including sums of infinite series, differentiation, and single and double integration. Our Approach Talking **with** students taking or having completed a beginning course in mathematical statistics reveals a major flaw in many courses. Students can take the course and leave it **with**out a clear understanding of the nature of statistics. Many see the theory as a collection of topics, weakly or strongly related, but fail to see that statistics is a theory of information **with** inference as its goal. Further, they may leave the course **with**out an understanding of the important role played by statistics in scientific investigations. These considerations led us to develop a text that differs from others in three ways: • First, the presentation of probability is preceded by a clear statement of the objective of statistics—statistical inference—and its role in scientific research. As students proceed through the theory of probability (Chapters 2 through 7), they are reminded frequently of the role that major topics play in statistical inference. The cumulative effect is that statistical inference is the dominating theme of the course. • The second feature of the text is connectivity. We explain not only how major topics play a role in statistical inference, but also how the topics are related to xiii

www.downloadslide.com xiv Preface one another. These integrating discussions appear most frequently in chapter introductions and conclusions. • Finally, the text is unique in its practical emphasis, both in exercises throughout the text and in the useful statistical methodological topics contained in Chapters 11–15, whose goal is to reinforce the elementary but sound theoretical foundation developed in the initial chapters. The book can be used in a variety of ways and adapted to the tastes of students and instructors. The difficulty of the material can be increased or decreased by controlling the assignment of exercises, by eliminating some topics, and by varying the amount of time devoted to each topic. A stronger applied flavor can be added by the elimination of some topics—for example, some sections of Chapters 6 and 7—and by devoting more time to the applied chapters at the end. Changes in the **Seventh** **Edition** Many students are visual learners who can profit from visual reinforcement of concepts and results. New to this edition is the inclusion of computer applets, all available for on line use at the Thomson website, www.thomsonedu.com/statistics/wackerly. Some of these applets are used to demonstrate statistical concepts, other applets permit users to assess the impact of parameter choices on the shapes of density functions, and the remainder of applets can be used to find exact probabilities and quantiles associated **with** gamma-, beta-, normal-, χ 2 -, t-, and F-distributed random variables—information of importance when constructing confidence intervals or performing tests of hypotheses. Some of the applets provide information available via the use of other software. Notably, the R language and environment for statistical computation and graphics (available free at http://www.r-project.org/) can be used to provide the quantiles and probabilities associated **with** the discrete and continuous distributions previously mentioned. The appropriate R commands are given in the respective sections of Chapters 3 and 4. The advantage of the applets is that they are “point and shoot,” provide accompanying graphics, and are considerably easier to use. However, R is vastly more powerful than the applets and can be used for many other statistical purposes. We leave other applications of R to the interested user or instructor. Chapter 2 introduces the first applet, Bayes’ Rule as a Tree, a demonstration that allows users to see why sometimes surprising results occur when Bayes’ rule is applied (see Figure 1). As in the sixth edition, maximum-likelihood estimates are introduced in Chapter 3 via examples for the estimates of the parameters of the binomial, geometric, and negative binomial distributions based on specific observed numerical values of random variables that possess these distributions. Follow-up problems at the end of the respective sections expand on these examples. In Chapter 4, the applet Normal Probabilities is used to compute the probability that any user-specified, normally distributed random variable falls in any specified interval. It also provides a graph of the selected normal density function and a visual reinforcement of the fact that probabilities associated **with** any normally distributed

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