Introduction to Probability

(2 reviews)

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Charles Grinstead, Swarthmore College
J. Laurie Snell, Dartmouth College

Pub Date: 1997

ISBN 13:

Publisher: American Mathematical Society

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Reviewed by Tomasz Gorecki, Visiting Professor, Colorado State University, on 1/8/2016.

The book consists of 12 chapters, 3 appendices with tables and index. It is designed for an introductory probability course, for use in a standard … read more

 

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Reviewed by Huimin Chen, associate professor, University of New Orleans, on 12/6/2016.

The book covers the fundamentals of probability theory with quite a few practical engineering applications, which seems appropriate for engineering … read more

 

Table of Contents

  • Chapter 1: Discrete Probability Distributions
  • Chapter 2: Continuous Probability Densities
  • Chapter 3: Combinatorics
  • Chapter 4: Conditional Probability
  • Chapter 5: Distributions and Densities
  • Chapter 6: Expected Value and Variance
  • Chapter 7: Sums of Random Variables
  • Chapter 8: Law of Large Numbers
  • Chapter 9: Central Limit Theorem
  • Chapter 10: Generating Functions
  • Chapter 11: Markov Chains
  • Chapter 12: Random Walks

About the Book

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a form understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

For use in a standard one-term course, in which both discrete and continuous probability is covered, students should have taken as a prerequisite two terms of calculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theory is necessary.

The text can also be used in a discrete probability course. The material has been organized in such a way that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization dispels an overly rigorous or formal view of probability and o?ers some strong pedagogical value in that the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. For use in a discrete probability course, students should have taken one term of calculus as a prerequisite.

Very little computing background is assumed or necessary in order to obtain full benefits from the use of the computing material and examples in the text. All of the programs that are used in the text have been written in each of the languages TrueBASIC, Maple, and Mathematica.

About the Contributors

Author(s)

Charles M. Grinstead, Professor, Department of Mathematics and Statistics, Swarthmore College.

James Laurie Snell, often cited as J. Laurie Snell, was an American mathematician. A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995.