A Modern Introduction to Probability and Statistics

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Authors:

• Frederik Michel Dekking ⁰ ,
• Cornelis Kraaikamp ¹ ,
• Hendrik Paul Lopuhaä ² ,
• …
• Ludolf Erwin Meester ³

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1. Frederik Michel Dekking

   1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
      

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2. Cornelis Kraaikamp

   1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
      

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3. Hendrik Paul Lopuhaä

   1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
      

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4. Ludolf Erwin Meester

   1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
      

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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.

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1. Front Matter

   Pages I-XV

   Download chapter PDF

2. Why probability and statistics?

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 1-11

3. Outcomes, events, and probability

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 13-24

4. Conditional probability and independence

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 25-40

5. Discrete random variables

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 41-55

6. Continuous random variables

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 57-70

7. Simulation

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 71-87

8. Expectation and variance

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 89-102

9. Computations with random variables

   • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

   Pages 103-114

10. Joint distributions and independence

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 115-134

11. Covariance and correlation

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 135-150

12. More computations with more random variables

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 151-166

13. The Poisson process

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 167-179

14. The law of large numbers

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 181-194

15. The central limit theorem

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 195-205

16. Exploratory data analysis: graphical summaries

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 207-230

17. Exploratory data analysis: numerical summaries

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 231-243

18. Basic statistical models

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 245-268

19. The bootstrap

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 269-284

20. Unbiased estimators

    • Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

    Pages 285-297

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From the reviews:

"[the material is] superbly motivated with interest-grabbing examples... exercises excellent and plentiful." Edward Williams, University of Michigan-Dearborn, USA

"... it is 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 inthe 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)

• Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

  Frederik Michel Dekking, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, Ludolf Erwin Meester

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.

• Analysis
• Estimator
• Random variable
• data analysis
• mathematical statistics
• simulation
• statistics

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