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Fundamentals of Probability: A First Course

  • Textbook
  • © 2010

Overview

Authors:
  1. Anirban DasGupta

    1. Dept. Statistics & Mathematics, Purdue University, West Lafayette, U.S.A.

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Part of the book series: Springer Texts in Statistics (STS)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introducing Probability

    • Anirban DasGupta
    Pages 1-21

  3. The Birthday and Matching Problems

    • Anirban DasGupta
    Pages 23-28

  4. Conditional Probability and Independence

    • Anirban DasGupta
    Pages 29-43

  5. Integer-Valued and Discrete Random Variables

    • Anirban DasGupta
    Pages 45-80

  6. Generating Functions

    • Anirban DasGupta
    Pages 81-90

  7. Standard Discrete Distributions

    • Anirban DasGupta
    Pages 91-125

  8. Continuous Random Variables

    • Anirban DasGupta
    Pages 127-169

  9. Some Special Continuous Distributions

    • Anirban DasGupta
    Pages 171-194

  10. Normal Distribution

    • Anirban DasGupta
    Pages 195-212

  11. Normal Approximations and the Central Limit Theorem

    • Anirban DasGupta
    Pages 213-242

  12. Multivariate Discrete Distributions

    • Anirban DasGupta
    Pages 243-273

  13. Multidimensional Densities

    • Anirban DasGupta
    Pages 275-319

  14. Convolutions and Transformations

    • Anirban DasGupta
    Pages 321-341

  15. Markov Chains and Applications

    • Anirban DasGupta
    Pages 343-378

  16. Urn Models in Physics and Genetics

    • Anirban DasGupta
    Pages 379-407

  17. Back Matter

    Pages 409-450
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Keywords

About this book

Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.

Reviews

From the reviews:

“Throughout the book, the author chooses examples and exercises that are classics in the field of probability … . does an admirable job of combining the rigor necessary for a first course in probability theory while continuing to engage the more applied oriented student’s curiosity with interesting examples and exercises. The book deserves serious consideration for anyone teaching the first course in probability theory or one engaged in applied work who desires a more thorough grounding in the mathematical principles of probability theory.” (Mark A. Mccomb, Technometrics, Vol. 54 (1), February, 2012)

“The present book is a text on the fundamentals of probability at an undergraduate and first-year graduate level for students in science, engineering and economics. … The book has an excellent set of examples and exercises and two appendices on supplementary homework, practice problems, symbols and formulas.” (Andreas N. Philippou, Zentralblatt MATH, Vol. 1211, 2011)

Authors and Affiliations

  • Dept. Statistics & Mathematics, Purdue University, West Lafayette, U.S.A.

    Anirban DasGupta

Bibliographic Information

  • Book Title: Fundamentals of Probability: A First Course

  • Authors: Anirban DasGupta

  • Series Title: Springer Texts in Statistics

  • DOI: https://doi.org/10.1007/978-1-4419-5780-1

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2010

  • Hardcover ISBN: 978-1-4419-5779-5Published: 09 April 2010

  • Softcover ISBN: 978-1-4614-2581-6Published: 27 May 2012

  • eBook ISBN: 978-1-4419-5780-1Published: 02 April 2010

  • Series ISSN: 1431-875X

  • Series E-ISSN: 2197-4136

  • Edition Number: 1

  • Number of Pages: XVI, 450

  • Topics: Probability Theory and Stochastic Processes

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