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  • Textbook
  • © 2009

Basic Probability Theory with Applications

Authors:

  • Presents elementary probability theory with interesting and well-chosen applications that illustrate the theory
  • Main results in elementary probability, random variables, random vectors and the central limit theorem are covered
  • Applications in reliability theory, basic queuing models, and time series are presented
  • Over 400 exercises reinforce the material and provide students with ample practice
  • Introductory chapter reviews the basic elements of differential calculus which are used in the material to follow
  • Includes supplementary material: sn.pub/extras
  • Request lecturer material: sn.pub/lecturer-material

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Table of contents (7 chapters)

  1. Front Matter

    Pages 1-13
  2. Review of differential calculus

    • Mario Lefebvre
    Pages 1-26
  3. Elementary probability

    • Mario Lefebvre
    Pages 27-53
  4. Random variables

    • Mario Lefebvre
    Pages 55-113
  5. Random vectors

    • Mario Lefebvre
    Pages 115-159
  6. Reliability

    • Mario Lefebvre
    Pages 161-190
  7. Queueing

    • Mario Lefebvre
    Pages 191-226
  8. Time series

    • Mario Lefebvre
    Pages 227-267
  9. Back Matter

    Pages 1-69

About this book

The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering. Chapters 2 to 4 cover the probability theory they generally need in their training. Although the treatment of the subject is surely su?cient for non-mathematicians, I intentionally avoided getting too much into detail. For instance, topics such as mixed type random variables and the Dirac delta function are only brie?y mentioned. Courses on probability theory are often considered di?cult. However, after having taught this subject for many years, I have come to the conclusion that one of the biggest problems that the students face when they try to learn probability theory, particularly nowadays, is their de?ciencies in basic di?erential and integral calculus. Integration by parts, for example, is often already forgotten by the students when they take a course on probability. For this reason, I have decided to write a chapter reviewing the basic elements of di?erential calculus. Even though this chapter might not be covered in class, the students can refer to it when needed. In this chapter, an e?ort was made to give the readers a good idea of the use in probability theory of the concepts they should already know. Chapter 2 presents the main results of what is known as elementary probability, including Bayes’ rule and elements of combinatorial analysis.

Authors and Affiliations

  • Dépt. Mathématiques et de, Ecole Polytechnique de Montréal, Montreal, Canada

    Mario Lefebvre

About the author



Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 84.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access