An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for "Probabilistic Sy An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for "Probabilistic Systems Analysis," an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students.
The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which an instructor can choose to match the goals of a particular course. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics.
The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
This introductory book provides the foundation for many other subjects in Science and Engineering, Economics, Business, and Finance, including those dealt with in our books Neuro-Dynamic Programming (Athena Scientific, 1996), Dynamic Programming and Optimal Control (Athena Scientific, 2007), and Stochastic Optimal Control: The Discrete-Time Case (Athena Scientific, 1996).
Book Features ．The 2nd Edition includes two new chapters with a thorough coverage of the central ideas of Bayesian and classical statistics. ．Develops the basic concepts of probability, random variables, stochastic processes, laws of large numbers, and the central limit theorem ．Illustrates the theory with many examples ．Provides many theoretical problems that extend the book's coverage and enhance its mathematical foundation (solutions are included in the text) ．Provides many problems that enhance the understanding of the basic material, together with web-posted solutions ．Is supplemented by additional web-based unsolved problems. ．Is coordinated with the material (syllabus, lecture slides, selection of homework, recitation, and tutorial problems) that is used in the MIT course (including lecture videos), and can help an instructor design his/her own course. ．Has been developed through extensive classroom use and experience at the Massachusetts Institute of Technology ...Continua Nascondi