Brief Course in Mathematical Statistics

For a one-semester course in Mathematical Statistics. This innovative new introduction to Mathematical Statistics covers the important concept of estimation at a point much earlier than other texts (Chapter 2). Thought-provoking pedagogical aids help students test their understanding and relate concepts to everyday life. Ideal for courses that offer a little less probability than usual, this book requires one year of calculus as a prerequisite. Almost all of the content in Chapters 1-3 and Sections 4.1-4.6 will likely be covered in a one-semester course, allowing the Instructor to select topics from Sections 4.7-4.11 and Chapters 5 and 6 to complete the course. * Content and Organization:- Chapter 1: With a little algebra of sets and a standard course in calculus as the mathematical background, some basic probability is presented in this chapter. - Chapter 2: Presents certain discrete distributions. Included are the topics of expectations, maximum likelihood estimation, as well as expectations and variances of linear functions, in particular those of the sample mean; and this makes it possible to introduce confidence intervals for means of distributions. Also included is a section on multivariate discrete distributions. (Early introduction of estimation is unique to this text.)- Chapter 3: Focuses on the continuous case and corresponding estimation problems. - Chapter 4: Includes some statistical inferences. Tests of statistical hypotheses and confidence intervals are tied together throughout. Material on linear regression is included. The section on distribution-free confidence intervals for percentiles also includes the topic of tolerance intervals. The last two sections concern chi-square tests. - Chapter 5: Provides computer applications. This chapter is devoted to a discussion of some uses of the computer both for data analysis and also for theoretical solutions such as simulation and bootstrapping. This is illustrated using Minitab for data analysis and Maple for theoretical solutions, simulations, and bootstrapping. (Other computer packages and Computer Algebra Systems could be used.) More than 100 probability and statistics procedures have been written for Maple. These are stored as stat.m along with some additional supplementary procedures stored as text files in "Maple Examples" that is available in an online web page: www.prenhall.com/statistics. Several statistical applications of Maple are included here. - Chapter 6: Introduces the moment-generating function. This allows the student to see how important theoretical results are proved. The Central Limit Theorem is explained and used in Chapters 3-6 with a proof of it given in this chapter. The use of order statistics in non-regular cases closes this chapter.* End pages - include summaries of the most important aspects of discrete distributions, continuous distributions, confidence intervals, and tests of hypotheses. * End-of-chapter Comments - Brief summaries provide some interesting aspects of probability and statistics. * Abundant Exercises - The average number of exercises is 11 per section with many exercises having several parts, giving instructors a wide selection for each assignment. * Wide range of fields used for examples, exercises, and applications:- Includes biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports. - In particular, the reader might be interested in those concerning insurance, Pap smear tests, estimating the number of whales in an ocean, fitting models, filling 12 ounce containers, environmental issues, and results in certain sporting events. "The authors have years of experience analyzing real data, have collected excellent examples to illustrate statistical concepts and anomalies, and are proven writers in the discipline." Professor Charles Sommer, SUNY College at Brockport "The authors have done a wonderful job in writing this book...I must congratulate them for doing a great job and helping in the development of the subject of Statistics." Professor M.L. Aggarwal, The University of Memphis