## Probability Models for Computer Science

**Author**: Sheldon M. Ross

**Publisher:**Taylor & Francis US

**ISBN:**9780125980517

**Category:**Computers

**Page:**288

**View:**9166

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The role of probability in computer science has been growing for years and, in lieu of a tailored textbook, many courses have employed a variety of similar, but not entirely applicable, alternatives. To meet the needs of the computer science graduate student (and the advanced undergraduate), best-selling author Sheldon Ross has developed the premier probability text for aspiring computer scientists involved in computer simulation and modeling. The math is precise and easily understood. As with his other texts, Sheldon Ross presents very clear explanations of concepts and covers those probability models that are most in demand by, and applicable to, computer science and related majors and practitioners. Many interesting examples and exercises have been chosen to illuminate the techniques presented Examples relating to bin packing, sorting algorithms, the find algorithm, random graphs, self-organising list problems, the maximum weighted independent set problem, hashing, probabilistic verification, max SAT problem, queuing networks, distributed workload models, and many othersMany interesting examples and exercises have been chosen to illuminate the techniques presented

## Probability and Statistics for Computer Scientists

**Author**: Michael Baron

**Publisher:**CRC Press

**ISBN:**1420011421

**Category:**Mathematics

**Page:**432

**View:**2512

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In modern computer science, software engineering, and other fields, the need arises to make decisions under uncertainty. Presenting probability and statistical methods, simulation techniques, and modeling tools, Probability and Statistics for Computer Scientists helps students solve problems and make optimal decisions in uncertain conditions, select stochastic models, compute probabilities and forecasts, and evaluate performance of computer systems and networks. After introducing probability and distributions, this easy-to-follow textbook provides two course options. The first approach is a probability-oriented course that begins with stochastic processes, Markov chains, and queuing theory, followed by computer simulations and Monte Carlo methods. The second approach is a more standard, statistics-emphasized course that focuses on statistical inference, estimation, hypothesis testing, and regression. Assuming one or two semesters of college calculus, the book is illustrated throughout with numerous examples, exercises, figures, and tables that stress direct applications in computer science and software engineering. It also provides MATLAB® codes and demonstrations written in simple commands that can be directly translated into other computer languages. By the end of this course, advanced undergraduate and beginning graduate students should be able to read a word problem or a corporate report, realize the uncertainty involved in the described situation, select a suitable probability model, estimate and test its parameters based on real data, compute probabilities of interesting events and other vital characteristics, and make appropriate conclusions and forecasts.

## Introduction to Probability Models

**Author**: Sheldon M. Ross

**Publisher:**Academic Press

**ISBN:**0124081215

**Category:**Mathematics

**Page:**784

**View:**7563

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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

## Linear Algebra and Probability for Computer Science Applications

**Author**: Ernest Davis

**Publisher:**CRC Press

**ISBN:**1466501553

**Category:**Mathematics

**Page:**431

**View:**4210

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Based on the author’s course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB® functions and features and give sample assignments in MATLAB; the author’s website provides the MATLAB code from the book. After an introductory chapter on MATLAB, the text is divided into two sections. The section on linear algebra gives an introduction to the theory of vectors, matrices, and linear transformations over the reals. It includes an extensive discussion on Gaussian elimination, geometric applications, and change of basis. It also introduces the issues of numerical stability and round-off error, the discrete Fourier transform, and singular value decomposition. The section on probability presents an introduction to the basic theory of probability and numerical random variables; later chapters discuss Markov models, Monte Carlo methods, information theory, and basic statistical techniques. The focus throughout is on topics and examples that are particularly relevant to computer science applications; for example, there is an extensive discussion on the use of hidden Markov models for tagging text and a discussion of the Zipf (inverse power law) distribution. Examples and Programming Assignments The examples and programming assignments focus on computer science applications. The applications covered are drawn from a range of computer science areas, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing, graph theory, scientific computing, decision theory, coding, cryptography, network analysis, data compression, and signal processing. Homework Problems Comprehensive problem sections include traditional calculation exercises, thought problems such as proofs, and programming assignments that involve creating MATLAB functions.

## Probability Models for Economic Decisions

**Author**: Roger B. Myerson

**Publisher:**Duxbury Press

**ISBN:**9780534423810

**Category:**Mathematics

**Page:**397

**View:**2277

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Learn to use probability in complex realistic situations with PROBABILITY MODELS FOR ECONOMIC DECISIONS. This introduction to the use of probability models for analyzing risks and economic decisions uses Microsoft Excel spreadsheets for the analytic work. As a result of the emphasis on spreadsheet modeling, you'll also develop sophisticated spreadsheet skills.

## Introduction to Probability and Statistics for Engineers and Scientists

**Author**: Sheldon M. Ross

**Publisher:**Academic Press

**ISBN:**0123948428

**Category:**Mathematics

**Page:**686

**View:**7723

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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.

## Probability and Statistics for Computer Science

**Author**: David Forsyth

**Publisher:**Springer

**ISBN:**3319644106

**Category:**Computers

**Page:**367

**View:**7198

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This textbook is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning. With careful treatment of topics that fill the curricular needs for the course, Probability and Statistics for Computer Science features: • A treatment of random variables and expectations dealing primarily with the discrete case. • A practical treatment of simulation, showing how many interesting probabilities and expectations can be extracted, with particular emphasis on Markov chains. • A clear but crisp account of simple point inference strategies (maximum likelihood; Bayesian inference) in simple contexts. This is extended to cover some confidence intervals, samples and populations for random sampling with replacement, and the simplest hypothesis testing. • A chapter dealing with classification, explaining why it’s useful; how to train SVM classifiers with stochastic gradient descent; and how to use implementations of more advanced methods such as random forests and nearest neighbors. • A chapter dealing with regression, explaining how to set up, use and understand linear regression and nearest neighbors regression in practical problems. • A chapter dealing with principal components analysis, developing intuition carefully, and including numerous practical examples. There is a brief description of multivariate scaling via principal coordinate analysis. • A chapter dealing with clustering via agglomerative methods and k-means, showing how to build vector quantized features for complex signals. Illustrated throughout, each main chapter includes many worked examples and other pedagogical elements such as boxed Procedures, Definitions, Useful Facts, and Remember This (short tips). Problems and Programming Exercises are at the end of each chapter, with a summary of what the reader should know. Instructor resources include a full set of model solutions for all problems, and an Instructor's Manual with accompanying presentation slides.

## Probability Models in Engineering and Science

**Author**: Haym Benaroya,Seon Mi Han,Mark Nagurka

**Publisher:**CRC Press

**ISBN:**9780824723156

**Category:**Science

**Page:**760

**View:**4474

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Certainty exists only in idealized models. Viewed as the quantification of uncertainties, probabilitry and random processes play a significant role in modern engineering, particularly in areas such as structural dynamics. Unlike this book, however, few texts develop applied probability in the practical manner appropriate for engineers. Probability Models in Engineering and Science provides a comprehensive, self-contained introduction to applied probabilistic modeling. The first four chapters present basic concepts in probability and random variables, and while doing so, develop methods for static problems. The remaining chapters address dynamic problems, where time is a critical parameter in the randomness. Highlights of the presentation include numerous examples and illustrations and an engaging, human connection to the subject, achieved through short biographies of some of the key people in the field. End-of-chapter problems help solidify understanding and footnotes to the literature expand the discussions and introduce relevant journals and texts. This book builds the background today's engineers need to deal explicitly with the scatter observed in experimental data and with intricate dynamic behavior. Designed for undergraduate and graduate coursework as well as self-study, the text's coverage of theory, approximation methods, and numerical methods make it equally valuable to practitioners.

## Probability Models

**Author**: John Haigh

**Publisher:**Springer Science & Business Media

**ISBN:**144715343X

**Category:**Mathematics

**Page:**287

**View:**3223

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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

**Category:**Mathematics

**Page:**224

**View:**3679

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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.

## Subjective Probability Models for Lifetimes

**Author**: Fabio Spizzichino

**Publisher:**CRC Press

**ISBN:**1420036130

**Category:**Mathematics

**Page:**272

**View:**8867

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Bayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjective Probability Models for Lifetimes details those differences and clarifies aspects of subjective probability that have a direct influence on modeling and drawing inference from failure and survival data. In particular, within a framework of Bayesian theory, the author considers the effects of different levels of information in the analysis of the phenomena of positive and negative aging. The author coherently reviews and compares the various definitions and results concerning stochastic ordering, statistical dependence, reliability, and decision theory. He offers a detailed but accessible mathematical treatment of different aspects of probability distributions for exchangeable vectors of lifetimes that imparts a clear understanding of what the "probabilistic description of aging" really is, and why it is important to analyzing survival and failure data.

## Probability Modeling and Computer Simulation

*An Integrated Introduction With Applications to Engineering and Computer Science*

**Author**: Norman S. Matloff

**Publisher:**Pws Publishing Company

**ISBN:**9780534918545

**Category:**Computers

**Page:**358

**View:**4757

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## Probability and Statistics for Computer Science

**Author**: James L. Johnson

**Publisher:**John Wiley & Sons

**ISBN:**1118165969

**Category:**Mathematics

**Page:**760

**View:**1290

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Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: "to present the mathematical analysis underlying probability results" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcement of content

## An Introduction to Mathematical Modeling

**Author**: Edward A. Bender

**Publisher:**Courier Corporation

**ISBN:**0486137120

**Category:**Mathematics

**Page:**272

**View:**2571

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Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

## Introduction to Probability Models, ISE

**Author**: Sheldon M. Ross

**Publisher:**Academic Press

**ISBN:**0080920179

**Category:**Mathematics

**Page:**800

**View:**7619

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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 and Statistics with Reliability, Queuing, and Computer Science Applications

**Author**: Kishor S. Trivedi

**Publisher:**John Wiley & Sons

**ISBN:**0471460818

**Category:**Computers

**Page:**880

**View:**7344

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An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

## Probabilistic Graphical Models

*Principles and Techniques*

**Author**: Daphne Koller,Nir Friedman

**Publisher:**MIT Press

**ISBN:**0262258358

**Category:**Computers

**Page:**1280

**View:**2265

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Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

## Performance Modeling and Design of Computer Systems

*Queueing Theory in Action*

**Author**: Mor Harchol-Balter

**Publisher:**Cambridge University Press

**ISBN:**1107027500

**Category:**Computers

**Page:**548

**View:**1548

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Written with computer scientists and engineers in mind, this book brings queueing theory decisively back to computer science.