Applied Probability and Statistics

1. Front Matter

   Pages i-xvii

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2. Introduction

   Pages 1-5

3. Elementary Probabilities

   Pages 7-53

4. Random Variables

   Pages 55-156

5. Random Vectors

   Pages 157-219

6. Stochastic Processes

   Pages 221-252

7. Estimation and Testing

   Pages 253-305

8. Simple Linear Regression

   Pages 307-338

9. Back Matter

   Pages 339-356

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This book is based mainly on the lecture notes that I have been using since 1993 for a course on applied probability for engineers that I teach at the Ecole Polytechnique de Montreal. This course is given to electrical, computer and physics engineering students, and is normally taken during the second or third year of their curriculum. Therefore, we assume that the reader has acquired a basic knowledge of differential and integral calculus. The main objective of this textbook is to provide a reference that covers the topics that every student in pure or applied sciences, such as physics, computer science, engineering, etc., should learn in probability theory, in addition to the basic notions of stochastic processes and statistics. It is not easy to find a single work on all these topics that is both succinct and also accessible to non-mathematicians. Because the students, who for the most part have never taken a course on prob­ ability theory, must do a lot of exercises in order to master the material presented, I included a very large number of problems in the book, some of which are solved in detail. Most of the exercises proposed after each chapter are problems written es­ pecially for examinations over the years. They are not, in general, routine problems, like the ones found in numerous textbooks.

• Mathematica
• Random variable
• Stochastic processes
• calculus
• classification
• linear regression
• probability
• statistics
• stochastic process

From the reviews:

"This textbook is appropriate for an undergraduate level course on probability theory and introductory statistics for an engineering department. The book can be recommended as a one- or two-semester undergraduate course book and also as a supplementary textbook for different advanced statistical courses. … The sections at the end of chapters contain exercises, problems and multiple choice questions. The style and contents of the book are well organized and make it easy to read." (Fazil A. Aliev, Mathematical Reviews, Issue 2007 b)

• Département de mathématiques et de génie industriel, École Polytechnique de Montréal, Québec, Montréal, Canada

  Mario Lefebvre

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