INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.
This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject.
The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level.
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, ...
Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided.
A bowl contains 12 red beads, 10 white beads, 25 blue beads, and three black beads. If one bead is drawn at random, what is the probability that it will be (a) blue; (b) red or white; (0) black; ((1) neither white nor black?
Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books Probability and Statistics are studied by ...
The statistician Karl Pearson analyzed a large number of outcomes at certain roulette tables and suggested that the wheels were biased. He wrote in 1894: Clearly, since the Casino does not serve the valuable end of huge laboratory for ...
... Practical Statistics for Medical Research D.G. Altman Probability — Methods and Measurement A. O'Hagan Problem Solving— A Statistician's Guide, Second Edition C. Chatfield Randomization, Bootstrap and Monte Carlo Methods in Biology, ...
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability.
The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional