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Introduction To Probability Models

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 0124081215
Size: 43.50 MB
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Introduction to Probability Models, Eleventh Edition is the latest version of Sheldon Ross's classic bestseller, used extensively by professionals and as the primary text for a first undergraduate course in applied probability. The book introduces the reader to elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research. The hallmark features of this text have been retained in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. The book contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams. It also presents new applications of probability models in biology and new material on Point Processes, including the Hawkes process. There is a list of commonly used notations and equations, along with an instructor's solutions manual. This text will be a helpful resource for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability. Updated data, and a list of commonly used notations and equations, instructor's solutions manual Offers new applications of probability models in biology and new material on Point Processes, including the Hawkes process Introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations research Covers finite capacity queues, insurance risk models, and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams Appropriate for a full year course, this book is written under the assumption that students are familiar with calculus

Introduction To Probability Models

Author: Sheldon M. Ross
Publisher: Elsevier
ISBN: 1483276589
Size: 52.82 MB
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Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena. This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula. Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated. This book is a good reference for students and researchers conducting work on probability models.

Introduction To Probability Models

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 9780123756879
Size: 65.42 MB
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Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text. The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students. This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes. New to this Edition: 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field Hallmark features: Superior writing style Excellent exercises and examples covering the wide breadth of coverage of probability topics Real-world applications in engineering, science, business and economics

Introduction To Probability Models Ise

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 0080920179
Size: 78.85 MB
Format: PDF, Mobi
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Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions. A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states. Simplified Approach for Analyzing Nonhomogeneous Poisson processes Additional results on queues relating to the (a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; (b) inspection paradox for M/M/1 queues (c) M/G/1 queue with server breakdown Many new examples and exercises.

Probability Models

Author: John Haigh
Publisher: Springer Science & Business Media
ISBN: 144715343X
Size: 36.54 MB
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The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

Applied Probability Models With Optimization Applications

Author: Sheldon M. Ross
Publisher: Courier Corporation
ISBN: 0486318648
Size: 33.10 MB
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Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.

Introduction To Probability And Statistics For Engineers And Scientists

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 0123948428
Size: 73.36 MB
Format: PDF, Kindle
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Introduction to Probability and Statistics for Engineers and Scientists provides a superior introduction to applied probability and statistics for engineering or science majors. Ross emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage. As with the previous editions, Ross' text has tremendously clear exposition, plus real-data examples and exercises throughout the text. Numerous exercises, examples, and applications connect probability theory to everyday statistical problems and situations. Clear exposition by a renowned expert author Real data examples that use significant real data from actual studies across life science, engineering, computing and business End of Chapter review material that emphasizes key ideas as well as the risks associated with practical application of the material 25% New Updated problem sets and applications, that demonstrate updated applications to engineering as well as biological, physical and computer science New additions to proofs in the estimation section New coverage of Pareto and lognormal distributions, prediction intervals, use of dummy variables in multiple regression models, and testing equality of multiple population distributions.

Introduction To Probability Models Eighth Edition

Author: Sheldon M. Ross
Publisher:
ISBN: 9780125980562
Size: 54.76 MB
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Introduction to Probability Models, 8th Edition, continues to introduce and inspire readers to the art of applying probability theory to phenomena in fields such as engineering, computer science, management and actuarial science, the physical and social sciences, and operations research. Now revised and updated, this best-selling book retains its hallmark intuitive, lively writing style, captivating introduction to applications from diverse disciplines, and plentiful exercises and worked-out examples. The 8th Edition includes five new sections and numerous new examples and exercises, many of which focus on strategies applicable in risk industries such as insurance or actuarial work. The five new sections include: * Section 3.6.4 presents an elementary approach, using only conditional expectation, for computing the expected time until a sequence of independent and identically distributed random variables produce a specified pattern. * Section 3.6.5 derives an identity involving compound Poisson random variables and then uses it to obtain an elegant recursive formula for the probabilities of compound Poisson random variables whose incremental increases are nonnegative and integer valued * Section 5.4.3 is concerned with a conditional Poisson process, a type of process that is widely applicable in the risk industries * Section 7.10 presents a derivation of and a new characterization for the classical insurance ruin probability. * Section 11.8 presents a simulation procedure known as coupling from the past; its use enables one to exactly generate the value of a random variable whose distribution is that of the stationary distribution of a given Markov chain, evenin cases where the stationary distribution cannot itself be explicitly determined. Other Academic Press books by Sheldon Ross: Simulation 3rd Ed., ISBN: 0-12-598053-1 Probability Models for Computer Science, ISBN 0-12-598051-5 Introduction to Probability and Statistics for Engineers and Scientists, 2nd Ed., ISBN: 0-12-598472-3 * Classic text by best-selling author * Continues the tradition of expository excellence * Contains compulsory material for Exam 3 of the Society of Actuaries

Introduction To Stochastic Dynamic Programming

Author: Sheldon M. Ross
Publisher: Academic Press
ISBN: 1483269094
Size: 36.42 MB
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Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.