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Mathematics 2006 - Probability
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David Williams, University of Wales, Swansea
In this lively look at both subjects, David Williams convinces Mathematics students of the intrinsic interest of Statistics and Probability, and Statistics students that the language of Mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications. Statistics chapters present both the Frequentist and Bayesian approaches, emphasizing Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modeling. C or WinBUGS code is provided for computational examples and simulations.
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David Stirzaker, University of Oxford
This fully revised and updated new edition of the well established textbook affords a clear introduction to the theory of probability. Topics covered include conditional probability, independence, discrete and continuous random variables, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous examples and exercises to help develop the important skills necessary for problem solving.
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Henk Tijms, Vrije Universiteit, Amsterdam
Mastering the concepts of probability can cast new light on situations in which randomness and chance appear to rule. With an emphasis on why probability works and how it can be applied, Henk Tijms introduces the reader to the world of probability in an informal way. Lotteries and casino games provide a natural source of motivation, and he carefully discusses these with many worked examples to illustrate the key concepts from probability theory.
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Yuri Suhov, University of Cambridge
Mark Kelbert, University of Wales, Swansea
Because probability and statistics are as much about intuition and problem solving, as they are about theorem proving, students can find it very difficult to make a successful transition from lectures to examinations and practice. Since the subject is critical in many modern applications, Yuri Suhov and Michael Kelbert have rectified deficiencies in traditional lecture-based methods, by combining a wealth of exercises for which they have supplied complete solutions. These solutions are adapted to needs and skills of students and include basic mathematical facts as needed.
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James R. Norris, University of Cambridge
In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.
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David Stirzaker, University of Oxford
This concise introduction to probability theory is written in an informal, tutorial style with concepts and techniques defined and developed as necessary. After an elementary discussion of chance, Stirzaker sets out the central and crucial rules and ideas of probability including independence and conditioning. Counting, combinatorics, and the ideas of probability distributions and densities follow. Later chapters present random variables and examine independence, conditioning, covariance, and functions of random variables, both discrete and continuous. The final chapter considers generating functions and applies this concept to practical problems including branching processes, random walks, and the central limit theorem. Examples, demonstrations, and exercises are used throughout to explore the ways in which probability is motivated by, and applied to, real life problems in science, medicine, gaming and other subjects of interest. Essential proofs of important results are included. Assuming minimal prior technical knowledge on the part of the reader, this book is suitable for students taking introductory courses in probability and will provide a solid foundation for more advanced courses in probability and statistics. It is also a valuable reference to those needing a working knowledge of probability theory and will appeal to anyone interested in this endlessly fascinating and entertaining subject.
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