Introduction to Probability

Introduction to Probability - Douglas G. Kelly - 9780023631450 - Mathematics Statistics - Statistics (100)
Prentice Hall
Douglas G. Kelly  
Total pages
November 1993
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Introduction to Probability
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Designed for post-calculus undergraduate probability courses.

This text thoroughly covers the concepts of probability, random variables, distributions, expected value, and the ramifications and applications of limit theorems. The text focuses on theory motivated by applications, especially in statistical inference and stochastic processes. Numerous examples and exercises accompany the text's accessible expository style. The author carefully builds student understanding by progressively reinforcing concepts and moving from concrete fundamentals to more abstract material. The topics are arranged so key concepts are introduced early. Standard distributions are introduced in the first chapter and are referred to throughout the book. The author's evenhanded treatment of this subject avoids overwhelming students in the first one or two chapters.


  • the text's unique topical organization introduces all important material early and reinforces it throughout.
  • introduces standard distributions gradually, first in examples and exercises, and refers to them throughout. Later in the text two chapters (Chs. 7 and 8) cover them for summary, review, and reference.
  • examples and exercises reinforce concepts and are extremely useful for review and self-evaluation.
  • the text avoids getting bogged-down by excessive higher-level mathematical details while still adequately preparing students who will continue in probability.
  • includes coverage of Poisson and Bernoulli processes, generating functions, conditioning, and Bayes' theorem for discrete and absolutely continuous random variables-topics often not covered in other texts.
  • contains many historical notes, exercises, and examples with a real- world focus that students will find pertinent and interesting.

Table of Contents

1. Probability Models: Definitions and Examples.

2. The Algebra of Events and Probabilities.

3. Probability Distributions.

4. Expected Values.

5. Functions of Random Variables.

6. Normal Distributions and the Central Limit Theorem.

7. Some Important Distributions on the Nonnegative Integers.

8. Some Important Absolutely Continuous Distributions.

9. Conditioning and Baye's Theorem for Random Variables.

Suggested Reading and Bibliography.

Appendix A. Review of Some Topics From Calculus and Set Theory.

Appendix B. Summaries of Commonly-used Distributions.

Appendix C. A Table of the Standard Normal Cumulative Distribution Function.