Probability And Conditional Expectation
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Probability And Conditional Expectation
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Author : Rolf Steyer
language : en
Publisher: John Wiley & Sons
Release Date : 2017-02-22
Probability And Conditional Expectation written by Rolf Steyer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-22 with Mathematics categories.
Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions. Probability and Conditional Expectations Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics. Explores the basics of random variables along with extensive coverage of measurable functions and integration. Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects. Is illustrated throughout with simple examples, numerous exercises and detailed solutions. Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.
Conditional Measures And Applications
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Author : M.M. Rao
language : en
Publisher: CRC Press
Release Date : 2005-05-25
Conditional Measures And Applications written by M.M. Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-25 with Mathematics categories.
In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and
Probability Via Expectation
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Author : Peter Whittle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Probability Via Expectation written by Peter Whittle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text rather than the author should persuade, and left the text to speak for itself. It has, indeed, stimulated a steady interest, to the point that Springer-Verlag has now commissioned this complete reworking.
Basic Probability Theory
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Author : Robert B. Ash
language : en
Publisher: Courier Corporation
Release Date : 2008-06-26
Basic Probability Theory written by Robert B. Ash and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-26 with Mathematics categories.
This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.
Probability
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Author : Robert P. Dobrow
language : en
Publisher: John Wiley & Sons
Release Date : 2013-10-16
Probability written by Robert P. Dobrow and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.
An introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability. With real-life examples and thoughtful exercises from fields as diverse as biology, computer science, cryptology, ecology, public health, and sports, the book is accessible for a variety of readers. The book’s emphasis on simulation through the use of the popular R software language clarifies and illustrates key computational and theoretical results. Probability: With Applications and R helps readers develop problem-solving skills and delivers an appropriate mix of theory and application. The book includes: Chapters covering first principles, conditional probability, independent trials, random variables, discrete distributions, continuous probability, continuous distributions, conditional distribution, and limits An early introduction to random variables and Monte Carlo simulation and an emphasis on conditional probability, conditioning, and developing probabilistic intuition An R tutorial with example script files Many classic and historical problems of probability as well as nontraditional material, such as Benford’s law, power-law distributions, and Bayesian statistics A topics section with suitable material for projects and explorations, such as random walk on graphs, Markov chains, and Markov chain Monte Carlo Chapter-by-chapter summaries and hundreds of practical exercises Probability: With Applications and R is an ideal text for a beginning course in probability at the undergraduate level.
Conditional Independence In Applied Probability
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Author : P.E. Pfeiffer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Conditional Independence In Applied Probability written by P.E. Pfeiffer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.
Introduction To Applied Probability
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Author : Paul E. Pfeiffer
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Introduction To Applied Probability written by Paul E. Pfeiffer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.
Elementary Probability
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Author : David Stirzaker
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-18
Elementary Probability written by David Stirzaker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-18 with Mathematics categories.
Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.
Introduction To Probability Theory A First Course On The Measure Theoretic Approach
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Author : Nima Moshayedi
language : en
Publisher: World Scientific
Release Date : 2022-03-23
Introduction To Probability Theory A First Course On The Measure Theoretic Approach written by Nima Moshayedi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-23 with Mathematics categories.
This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part. /description --
Probability Through Problems
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Author : Marek Capinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Probability Through Problems written by Marek Capinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus.