Applied Probability
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Applied Probability
Author: Frank A. Haight
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
Probability (including stochastic processes) is now being applied to virtually every academic discipline, especially to the sciences. An area of substantial application is that known as operations research or industrial engineering, which incorporates subjects such as queueing theory, optimization, and network flow. This book provides a compact introduction to that field for students with minimal preparation, knowing mainly calculus and having "mathe matical maturity." Beginning with the basics of probability, the develop ment is self-contained but not abstract, that is, without measure theory and its probabilistic counterpart. Although the text is reasonably short, a course based on this book will normally occupy two semesters or three quarters. There are many points in the discussions and problems which require the assistance of an instructor for completeness and clarity. The book is designed to give equal emphasis to those applications which motivate the subject and to appropriatemathematical techniques. Thus, the student who has successfully completed the course is ready to turn in either of two directions: towards direct study of research papers in operations research, or towards a course in abstract probability, for which this text provides the intuitive background. Frank A. Haight Pennsylvania State University vii Contents 1. Discrete Probability .................................................. 1 1.1. Applied Probability. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Sample Spaces ......................................................... 3 1.3. Probability Distributions and Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4. The Connection between Distributions and Sample Points: Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . .
Applied Probability
Author: Kenneth Lange
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-01-17
Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.
Applied Probability and Statistics
Author: Mario Lefebvre
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-04-03
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.