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Macmillan Higher Education Palgrave Higher Education

A Modern Introduction to Probability and Statistics

Understanding Why and How

ISBN 9781852338961
Publication Date June 2005
Formats Hardcover Paperback Ebook 
Publisher Springer

Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. 

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap.

Michel Dekking, Cor Kraaikamp, Rik Lopuhaä and Ludolf Meester are professors in the Department of Applied Mathematics at TU Delft, The Netherlands. The material in this book has been successfully taught there for several years, and at the University of Leiden, The Netherlands, and Wesleyan University, USA, since 2003.

Why probability and statistics?
Outcomes, events, and probability
Conditional probability and independence
Discrete random variables
Continuous random variables
Expectation and variance
Computations with random variables
Joint distributions and independence
Covariance and correlation
More computations with more random variables
The Poisson process
The law of large numbers
The central limit theorem
Exploratory data analysis: graphical summaries
Exploratory data analysis: numerical summaries
Basic statistical models
The bootstrap
Unbiased estimators
Efficiency and mean squared error
Maximum likelihood
The method of least squares
Confidence intervals for the mean
More on confidence intervals
Testing hypotheses: essentials
Testing hypotheses: elaboration
The t-test
Comparing two samples.


From the reviews: "[the material is] superbly motivated with interest-grabbing examples... exercises excellent and plentiful." Edward Williams, University of Michigan-Dearborn, USA "... itis a notoriously hard task to introduce probability and statistics with a mix of intuition and mathematics to keep students motivated. Therefore, I very much welcome this book and recommend it as course material." Sara van de Geer, Leiden University, The Netherlands "This textbook provides a well-written first course in probability and statistics...It is a book that has been written based on the long teaching experience of the authors and I would certainly recommend it for university coursework." Short Book Reviews of the International Statistical Institute, December 2005 "This book has numerous quick exercises to give direct feedback to the students. … A website at www.springeronline.com/978-1-85233-896-1 gives access to the data files used in the text … . This will be a key text for undergraduates in computer science, physics, mathematics, chemistry, biology and business studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects." (Rainer Beedgen, Zentralblatt MATH, Vol. 1079, 2006) "The book is designed for a one-semester introductory course in probability and statistics basics for engineering students. … It can also be used by students in other more mathematically oriented majors such as applied mathematics with more emphasis on the mathematics and additional coverage in topics such as combinatorics, conditional expectation, and generating functions. … More elaborate exercises and real datasets are given at the end of each chapter." (Arthur B. Yeh, Technometrics, Vol. 49 (3), August, 2007)
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