This book moves systematically through the topic of applied probability from an introductory chapter to random variables and vectors, stochastic processes, estimation, testing and regression and more. Includes solved and unsolved problems, review questions, and historical notes on the mathematicians mentioned throughout.
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.
Inhaltsverzeichnis Introduction. - Elementary Probabilities. - Random Variables. - Random Vectors. - Stochastic Processes. - Estimation and Testing. - Simple Linear Regression. - Appendices: Mathematical Formulas. - Quantiles Sampling Distributions. - Classification of the Exercises. - Answers Multiple Choice Questions. - Answers to Selected Exercises.