Modern Mathematical Statistics with Applications: Edition 2

Springer Science & Business Media
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Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data.

The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics. Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters. The remainder of the book explores the use of this methodology in a variety of more complex settings.

This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature.

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About the author

Jay Devore received a B.S. in Engineering Science from the University of California, Berkeley, and a Ph.D. in Statistics from Stanford University. He previously taught at the University of Florida and Oberlin College, and has had visiting positions at Stanford, Harvard, the University of Washington, New York University, and Columbia. He has been at California Polytechnic State University, San Luis Obispo, since 1977, where he was chair of the Department of Statistics for seven years and recently achieved the exalted status of Professor Emeritus.

Jay has previously authored or coauthored five other books, including Probability and Statistics for Engineering and the Sciences, which won a McGuffey Longevity Award from the Text and Academic Authors Association for demonstrated excellence over time . He is a Fellow of the American Statistical Association, has been an associate editor for both the Journal of the American Statistical Association and The American Statistician, and received the Distinguished Teaching Award from Cal Poly in 1991. His recreational interests include reading, playing tennis, traveling, and cooking and eating good food.

Ken Berk has a B.S. in Physics from Carnegie Tech (now Carnegie Mellon) and a Ph.D. in Mathematics from the University of Minnesota. He is Professor Emeritus of Mathematics at Illinois State University and a Fellow of the American Statistical Association. He founded the Software Reviews section of The American Statistician and edited it for six years. He served as secretary/treasurer, program chair, and chair of the Statistical Computing Section of the American Statistical Association, and he twice co-chaired the Interface Symposium, the main annual meeting in statistical computing. His published work includes papers on time series, statistical computing, regression analysis, and statistical graphics, as well as the book Data Analysis with Microsoft Excel (with Patrick Carey).

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Additional Information

Springer Science & Business Media
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Published on
Dec 7, 2011
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Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
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Content Protection
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An introduction to probability at the undergraduate level

Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability.

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Probability: With Applications and R helps readers develop problem-solving skills and delivers an appropriate mix of theory and application. The book includes:

Chapters covering first principles, conditional probability, independent trials, random variables, discrete distributions, continuous probability, continuous distributions, conditional distribution, and limits An early introduction to random variables and Monte Carlo simulation and an emphasis on conditional probability, conditioning, and developing probabilistic intuition An R tutorial with example script files Many classic and historical problems of probability as well as nontraditional material, such as Benford’s law, power-law distributions, and Bayesian statistics A topics section with suitable material for projects and explorations, such as random walk on graphs, Markov chains, and Markov chain Monte Carlo Chapter-by-chapter summaries and hundreds of practical exercises

Probability: With Applications and R is an ideal text for a beginning course in probability at the undergraduate level.

Introducing the tools of statistics and probability from the ground up

An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences.

Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features:

• Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices

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This updated and revised first-course textbook in applied probability provides a contemporary and lively post-calculus introduction to the subject of probability. The exposition reflects a desirable balance between fundamental theory and many applications involving a broad range of real problem scenarios. It is intended to appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and those business and social science majors interested in the quantitative aspects of their disciplines.

The textbook contains enough material for a year-long course, though many instructors will use it for a single term (one semester or one quarter). As such, three course syllabi with expanded course outlines are now available for download on the book’s page on the Springer website.

A one-term course would cover material in the core chapters (1-4), supplemented by selections from one or more of the remaining chapters on statistical inference (Ch. 5), Markov chains (Ch. 6), stochastic processes (Ch. 7), and signal processing (Ch. 8—available exclusively online and specifically designed for electrical and computer engineers, making the book suitable for a one-term class on random signals and noise).

For a year-long course, core chapters (1-4) are accessible to those who have taken a year of univariate differential and integral calculus; matrix algebra, multivariate calculus, and engineering mathematics are needed for the latter, more advanced chapters.

At the heart of the textbook’s pedagogy are 1,100 applied exercises, ranging from straightforward to reasonably challenging, roughly 700 exercises in the first four “core” chapters alone—a self-contained textbook of problems introducing basic theoretical knowledge necessary for solving problems and illustrating how to solve the problems at hand – in R and MATLAB, including code so that students can create simulations.

New to this edition

• Updated and re-worked Recommended Coverage for instructors, detailing which courses should use the textbook and how to utilize different sections for various objectives and time constraints

• Extended and revised instructions and solutions to problem sets

• Overhaul of Section 7.7 on continuous-time Markov chains

• Supplementary materials include three sample syllabi and updated solutions manuals for both instructors and students

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