#### Jane M. Horgan Probability with R

Provides a comprehensive introduction to probability with an emphasis on computing-related applications This self-contained new and extended edition outlines a first course in probability applied to computer-related disciplines. As in the first edition, experimentation and simulation are favoured over mathematical proofs. The freely down-loadable statistical programming language R is used throughout the text, not only as a tool for calculation and data analysis, but also to illustrate concepts of probability and to simulate distributions. The examples in Probability with R: An Introduction with Computer Science Applications, Second Edition cover a wide range of computer science applications, including: testing program performance; measuring response time and CPU time; estimating the reliability of components and systems; evaluating algorithms and queuing systems. Chapters cover: The R language; summarizing statistical data; graphical displays; the fundamentals of probability; reliability; discrete and continuous distributions; and more. This second edition includes: improved R code throughout the text, as well as new procedures, packages and interfaces; updated and additional examples, exercises and projects covering recent developments of computing; an introduction to bivariate discrete distributions together with the R functions used to handle large matrices of conditional probabilities, which are often needed in machine translation; an introduction to linear regression with particular emphasis on its application to machine learning using testing and training data; a new section on spam filtering using Bayes theorem to develop the filters; an extended range of Poisson applications such as network failures, website hits, virus attacks and accessing the cloud; use of new allocation functions in R to deal with hash table collision, server overload and the general allocation problem. The book is supplemented with a Wiley Book Companion Site featuring data and solutions to exercises within the book. Primarily addressed to students of computer science and related areas, Probability with R: An Introduction with Computer Science Applications, Second Edition is also an excellent text for students of engineering and the general sciences. Computing professionals who need to understand the relevance of probability in their areas of practice will find it useful.

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Подробнее#### Jane M. Horgan Probability with R

Provides a comprehensive introduction to probability with an emphasis on computing-related applications This self-contained new and extended edition outlines a first course in probability applied to computer-related disciplines. As in the first edition, experimentation and simulation are favoured over mathematical proofs. The freely down-loadable statistical programming language R is used throughout the text, not only as a tool for calculation and data analysis, but also to illustrate concepts of probability and to simulate distributions. The examples in Probability with R: An Introduction with Computer Science Applications, Second Edition cover a wide range of computer science applications, including: testing program performance; measuring response time and CPU time; estimating the reliability of components and systems; evaluating algorithms and queuing systems. Chapters cover: The R language; summarizing statistical data; graphical displays; the fundamentals of probability; reliability; discrete and continuous distributions; and more. This second edition includes: improved R code throughout the text, as well as new procedures, packages and interfaces; updated and additional examples, exercises and projects covering recent developments of computing; an introduction to bivariate discrete distributions together with the R functions used to handle large matrices of conditional probabilities, which are often needed in machine translation; an introduction to linear regression with particular emphasis on its application to machine learning using testing and training data; a new section on spam filtering using Bayes theorem to develop the filters; an extended range of Poisson applications such as network failures, website hits, virus attacks and accessing the cloud; use of new allocation functions in R to deal with hash table collision, server overload and the general allocation problem. The book is supplemented with a Wiley Book Companion Site featuring data and solutions to exercises within the book. Primarily addressed to students of computer science and related areas, Probability with R: An Introduction with Computer Science Applications, Second Edition is also an excellent text for students of engineering and the general sciences. Computing professionals who need to understand the relevance of probability in their areas of practice will find it useful.

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Подробнее#### Группа авторов Probability with R

A Complete Introduction to probability AND its computer Science Applications USING R Probability with R serves as a comprehensive and introductory book on probability with an emphasis on computing-related applications. Real examples show how probability can be used in practical situations, and the freely available and downloadable statistical programming language R illustrates and clarifies the book's main principles. Promoting a simulation- and experimentation-driven methodology, this book highlights the relationship between probability and computing in five distinctive parts: The R Language presents the essentials of the R language, including key procedures for summarizing and building graphical displays of statistical data. Fundamentals of Probability provides the foundations of the basic concepts of probability and moves into applications in computing. Topical coverage includes conditional probability, Bayes' theorem, system reliability, and the development of the main laws and properties of probability. Discrete Distributions addresses discrete random variables and their density and distribution functions as well as the properties of expectation. The geometric, binomial, hypergeometric, and Poisson distributions are also discussed and used to develop sampling inspection schemes. Continuous Distributions introduces continuous variables by examining the waiting time between Poisson occurrences. The exponential distribution and its applications to reliability are investigated, and the Markov property is illustrated via simulation in R. The normal distribution is examined and applied to statistical process control. Tailing Off delves into the use of Markov and Chebyshev inequalities as tools for estimating tail probabilities with limited information on the random variable. Numerous exercises and projects are provided in each chapter, many of which require the use of R to perform routine calculations and conduct experiments with simulated data. The author directs readers to the appropriate Web-based resources for installing the R software package and also supplies the essential commands for working in the R workspace. A related Web site features an active appendix as well as a forum for readers to share findings, thoughts, and ideas. With its accessible and hands-on approach, Probability with R is an ideal book for a first course in probability at the upper-undergraduate and graduate levels for readers with a background in computer science, engineering, and the general sciences. It also serves as a valuable reference for computing professionals who would like to further understand the relevance of probability in their areas of practice.

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Подробнее#### Robert P. Dobrow Probability

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.

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Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusion-exclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniform probability, the inclusion-exclusion principle, independence and convergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra.

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Подробнее#### Prabhanjan N. Tattar A Course in Statistics with R

Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical concepts Provides graphical presentations inclusive of mathematical expressions Aids understanding of limit theorems of probability with and without the simulation approach Presents detailed algorithmic development of statistical models from scratch Includes practical applications with over 50 data sets

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Explores computer-intensive probability and statistics for ecosystem management decision making Simulation is an accessible way to explain probability and stochastic model behavior to beginners. This book introduces probability and statistics to future and practicing ecosystem managers by providing a comprehensive treatment of these two areas. The author presents a self-contained introduction for individuals involved in monitoring, assessing, and managing ecosystems and features intuitive, simulation-based explanations of probabilistic and statistical concepts. Mathematical programming details are provided for estimating ecosystem model parameters with Minimum Distance, a robust and computer-intensive method. The majority of examples illustrate how probability and statistics can be applied to ecosystem management challenges. There are over 50 exercises – making this book suitable for a lecture course in a natural resource and/or wildlife management department, or as the main text in a program of self-study. Key features: Reviews different approaches to wildlife and ecosystem management and inference. Uses simulation as an accessible way to explain probability and stochastic model behavior to beginners. Covers material from basic probability through to hierarchical Bayesian models and spatial/ spatio-temporal statistical inference. Provides detailed instructions for using R, along with complete R programs to recreate the output of the many examples presented. Provides an introduction to Geographic Information Systems (GIS) along with examples from Quantum GIS, a free GIS software package. A companion website featuring all R code and data used throughout the book. Solutions to all exercises are presented along with an online intelligent tutoring system that supports readers who are using the book for self-study.

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Jane M. Horgan is Associate Professor of Statistics in the School of Computing at Dublin City University, Ireland. A Fellow of the Institute of Statisticians, Dr. Horgan has published extensively in the areas of statistical sampling and estimation. Her research interests include applications to both financial auditing and rare incidence skewed ...

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Jane M. Horgan Dublin City University, Ireland jane.horgan@dcu.ie We outline the role of the open-source statistical programming environment R (R Development Core Team, 2005) in teaching a first course in probability. We show how R, which is freely available and downloadable from the web, may be used not only as a tool for calculation and data analysis, but also to illustrate probability ...

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Jane M. Horgan is Associate Professor of Statistics in the School of Computing at Dublin City University, Ireland. A Fellow of the Institute of Statisticians, Dr. Horgan has published extensively in the areas of statistical sampling and estimation. Her research interests include applications to both financial auditing and rare incidence skewed populations.

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JANE M. HORGAN is Emeritus Professor of Statistics in the School of Computing, Dublin City University, Ireland. A Fellow of the Institute of Statisticians, she graduated in Statistics with a First Class Honours from University College Cork and completed postgraduate work at the London School of Economics and at London City University. Dr. Horgan has published extensively in statistics and computing.

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#### A Tutorial on Probability Theory

Probability measures the amount of uncertainty of an event: a fact whose occurrence is uncertain. Consider, as an example, the event R “Tomorrow, January 16th, it will rain in Amherst”. The occurrence of R is diﬃcult to predict — we have all been victims of wrong forecasts made by the “weather channel” — and we quantify this uncertainty with a number p(R), called the probability ...

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probability of Aoccurring is the sum of probabilities of all these subsets occur-ring. We say that two events Aand Bare independent if Pr(A)does not depend on whether Boccurs or not, and Pr(B)does not depend on whether Aoccurs or not. If events Aand Bare independent, then their joint probability, that is, the probability that both Aand Boccur is: Pr(AB)=Pr(A)Pr(B) That is, it is the product of ...

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interest in probability theory was stimulated ﬁrst by reading the work of Harold Jeffreys (1939) and realizing that his viewpoint makes all the problems of theoretical physics appear in a very different light. But then, in quick succession, discovery of the work of R. T. Cox (1946), Shannon (1948) and P´olya (1954) opened up new worlds of thought, whose explo- ration has occupied my mind ...

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Подробнее#### Bhisham C. Gupta Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP

Introduces basic concepts in probability and statistics to data science students, as well as engineers and scientists Aimed at undergraduate/graduate-level engineering and natural science students, this timely, fully updated edition of a popular book on statistics and probability shows how real-world problems can be solved using statistical concepts. It removes Excel exhibits and replaces them with R software throughout, and updates both MINITAB and JMP software instructions and content. A new chapter discussing data mining—including big data, classification, machine learning, and visualization—is featured. Another new chapter covers cluster analysis methodologies in hierarchical, nonhierarchical, and model based clustering. The book also offers a chapter on Response Surfaces that previously appeared on the book’s companion website. Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP, Second Edition is broken into two parts. Part I covers topics such as: describing data graphically and numerically, elements of probability, discrete and continuous random variables and their probability distributions, distribution functions of random variables, sampling distributions, estimation of population parameters and hypothesis testing. Part II covers: elements of reliability theory, data mining, cluster analysis, analysis of categorical data, nonparametric tests, simple and multiple linear regression analysis, analysis of variance, factorial designs, response surfaces, and statistical quality control (SQC) including phase I and phase II control charts. The appendices contain statistical tables and charts and answers to selected problems. Features two new chapters—one on Data Mining and another on Cluster Analysis Now contains R exhibits including code, graphical display, and some results MINITAB and JMP have been updated to their latest versions Emphasizes the p-value approach and includes related practical interpretations Offers a more applied statistical focus, and features modified examples to better exhibit statistical concepts Supplemented with an Instructor's-only solutions manual on a book’s companion website Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP is an excellent text for graduate level data science students, and engineers and scientists. It is also an ideal introduction to applied statistics and probability for undergraduate students in engineering and the natural sciences.

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Подробнее#### Bhisham C. Gupta Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP

Introduces basic concepts in probability and statistics to data science students, as well as engineers and scientists Aimed at undergraduate/graduate-level engineering and natural science students, this timely, fully updated edition of a popular book on statistics and probability shows how real-world problems can be solved using statistical concepts. It removes Excel exhibits and replaces them with R software throughout, and updates both MINITAB and JMP software instructions and content. A new chapter discussing data mining—including big data, classification, machine learning, and visualization—is featured. Another new chapter covers cluster analysis methodologies in hierarchical, nonhierarchical, and model based clustering. The book also offers a chapter on Response Surfaces that previously appeared on the book’s companion website. Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP, Second Edition is broken into two parts. Part I covers topics such as: describing data graphically and numerically, elements of probability, discrete and continuous random variables and their probability distributions, distribution functions of random variables, sampling distributions, estimation of population parameters and hypothesis testing. Part II covers: elements of reliability theory, data mining, cluster analysis, analysis of categorical data, , nonparametric tests, simple and multiple linear regression analysis, analysis of variance, factorial designs, response surfaces, and statistical quality control (SQC) including phase I and phase II control charts. The appendices contain statistical tables and charts and answers to selected problems. Features two new chapters—one on Data Mining and another on Cluster Analysis Now contains R exhibits including code, graphical display, and some results MINITAB and JMP have been updated to their latest versions Emphasizes the p-value approach and includes related practical interpretations Offers a more applied statistical focus, and features modified examples to better exhibit statistical concepts Supplemented with an Instructor's-only solutions manual on a book’s companion website Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP is an excellent text for graduate level data science students, and engineers and scientists. It is also an ideal introduction to applied statistics and probability for undergraduate students in engineering and the natural sciences.

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Подробнее#### Daniele Martini De Success Probability Estimation with Applications to Clinical Trials

Provides an introduction to the various statistical techniques involved in medical research and drug development with a focus on estimating the success probability of an experiment Success Probability Estimation with Applications to Clinical Trials details the use of success probability estimation in both the planning and analyzing of clinical trials and in widely used statistical tests. Devoted to both statisticians and non-statisticians who are involved in clinical trials, Part I of the book presents new concepts related to success probability estimation and their usefulness in clinical trials, and each section begins with a non-technical explanation of the presented concepts. Part II delves deeper into the techniques for success probability estimation and features applications to both reproducibility probability estimation and conservative sample size estimation. Success Probability Estimation with Applications to Clinical Trials: • Addresses the theoretical and practical aspects of the topic and introduces new and promising techniques in the statistical and pharmaceutical industries Features practical solutions for problems that are often encountered in clinical trials Includes success probability estimation for widely used statistical tests, such as parametric and nonparametric models Focuses on experimental planning, specifically the sample size of clinical trials using phase II results and data for planning phase III trials Introduces statistical concepts related to success probability estimation and their usefulness in clinical trials Success Probability Estimation with Applications to Clinical Trials is an ideal reference for statisticians and biostatisticians in the pharmaceutical industry as well as researchers and practitioners in medical centers who are actively involved in health policy, clinical research, and the design and evaluation of clinical trials.

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#### Ionut Florescu Probability and Stochastic Processes

A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book’s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.

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Подробнее#### Venkatarama Krishnan Probability and Random Processes

The second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions This book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions. Additional features of the second edition of Probability and Random Processes are: Updated chapters with new sections on Newton-Pepys’ problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations A new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra An eighth appendix examining the computation of the roots of discrete probability-generating functions With new material on theory and applications of probability, Probability and Random Processes, Second Edition is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.

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