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Introduction to Probability

(5 reviews)

Charles Grinstead, Swarthmore College

J. Laurie Snell, Dartmouth College

Pub Date: 1997

Publisher: American Mathematical Society

Language: English

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Reviewed by XIAOQIAN SUN, Professor, Clemson University on 2/2/18

The book covers all subjects that I need except the required materials on joint distributions. It would be great to have two more chapters to cover joint probability distributions for discrete and continuous random variables. Also I feel that the... read more

 

Reviewed by Steve Schoenbaechler, Instructor, Miami University (Ohio) on 6/21/17

There is a table of contents that breaks up the chapters into subtopics, also. There is an index. Not much depth in some areas. There isn't much talked about with certain graphics, aka defining histograms and pie charts. Hypothesis testing is... read more

 

Reviewed by Hasan Hamdan, Professor of Statistics, James Madison University on 6/21/17

The book covers all areas in a typical introductory probability course. The course would be appropriate for seniors in mathematics or statistics or data science or computer science. It is also appropriate for first year graduate students in any... read more

 

Reviewed by Huimin Chen, associate professor, University of New Orleans on 12/6/16

The book covers the fundamentals of probability theory with quite a few practical engineering applications, which seems appropriate for engineering students to connect the theory to the practice. Each chapter contains realistic examples that apply... read more

 

Reviewed by Tomasz Gorecki, Visiting Professor, Colorado State University on 1/8/16

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 one-term course, in which both discrete and continuous probability is covered. This book covers a... 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 continuedto 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 scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting 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 andtechniques necessary for a form understanding of the subject. The text can be usedin a variety of course lengths, levels, and areas of emphasis.

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

The text can also be used in a discrete probability course. The material has beenorganized in such a way that the discrete and continuous probability discussions arepresented in a separate, but parallel, manner. This organization dispels an overlyrigorous or formal view of probability and o?ers some strong pedagogical valuein that the discrete discussions can sometimes serve to motivate the more abstractcontinuous probability discussions. For use in a discrete probability course, studentsshould have taken one term of calculus as a prerequisite.

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

About the Contributors

Authors

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.