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Mathematical Statistics with Applications

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This textbook is of an interdisciplinary nature and is designed for a two- or one-semester course in probability and statistics, with basic calculus as a prerequisite. The book is primarily written to give a sound theoretical introduction to statistics while emphasizing applications. If teaching statistics is the main purpose of a two-semester course in probability and statistics, this textbook covers all the probability concepts necessary for the theoretical development of statistics in two chapters, and goes on to cover all major aspects of statistical theory in two semesters, instead of only a portion of statistical concepts. What is more, using the optional section on computer examples at the end of each chapter, the student can also simultaneously learn to utilize statistical software packages for data analysis. It is our aim, without sacrificing any rigor, to encourage students to apply the theoretical concepts they have learned. There are many examples and exercises concerning diverse application areas that will show the pertinence of statistical methodology to solving real-world problems. The examples with statistical software and projects at the end of the chapters will provide good perspective on the usefulness of statistical methods. To introduce the students to modern and increasingly popular statistical methods,we have introduced separate chapters on Bayesian analysis and empirical methods.

One of the main aims of this book is to prepare advanced undergraduates and beginning graduate students in the theory of statistics with emphasis on interdisciplinary applications. The audience for this course is regular full-time students from mathematics, statistics, engineering, physical sciences, business, social sciences, materials science, and so forth. Also, this textbook is suitable for people who work in industry and in education as a reference book on introductory statistics for a good theoretical foundation with clear indication of how to use statistical methods. Traditionally, one of the main prerequisites for this course is a semester of the introduction to probability theory. Aworking knowledge of elementary (descriptive) statistics is also a must. In schools where there is no statistics major, imposing such a background, in addition to calculus sequence, is very difficult. Most of the present books available on this subject contain full one-semester material for probability and then, based on those results, continue on to the topics in statistics. Also, some of these books include in their subject matter only the theory of statistics, whereas others take the cookbook approach of covering the mechanics. Thus, even with two full semesters of work, many basic and important concepts in statistics are never covered. This book has been written to remedy this problem. We fuse together both concepts in order for students to gain knowledge of the theory and at the same time develop the expertise to use their knowledge in real-world situations.
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