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Introduction To Probability

Author: Joseph K. Blitzstein
Publisher: CRC Press
ISBN: 146657559X
Size: 35.52 MB
Format: PDF
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Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Introduction To Probability With R

Author: Kenneth Baclawski
Publisher: CRC Press
ISBN: 9781420065220
Size: 36.80 MB
Format: PDF, Kindle
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Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.

Statistik Ii F R Dummies

Author: Deborah J. Rumsey
Publisher: John Wiley & Sons
ISBN: 3527669248
Size: 24.29 MB
Format: PDF, Mobi
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Vom Absolutrang bis zum Zweifach-Varianzanalysemodell – alles, was Sie über weiterführende Statistik wissen sollten Es gibt Qualen, große Qualen und Statistik, so sehen es viele Studenten. Mit diesem Buch lernen Sie weiterführende Statistik so leicht wie möglich. Deborah Rumsey zeigt Ihnen, wie Sie Varianzanalysen und Chi-Quadrat-Tests berechnen, wie Sie mit Regressionen arbeiten, ein Modell erstellen, Korrelationen bilden, nichtparametrische Prozeduren durchführen und vieles mehr. Aber auch die Grundlagen der Statistik bleiben nicht außen vor und deshalb erklärt Ihnen die Autorin, was Sie zu Mittelwerten, Vertrauensintervallen und Co wissen sollten. So lernen Sie die Methoden, die Sie brauchen, und erhalten das Handwerkszeug, um erfolgreich Ihre Statistikprüfungen zu bestehen. Sie erfahren: • Wie Sie mit multiplen Regressionen umgehen • Was es mit dem Vorzeichentest und dem Vorzeichenrangtest auf sich hat • Wie Sie sich innerhalb der statistischen Techniken zurechtfinden • Was das richtige Regressionsmodell für Ihre Analyse ist • Wie Regression und ANOVA zusammenhängen

Introduction To The Theory Of Statistical Inference

Author: Hannelore Liero
Publisher: CRC Press
ISBN: 1466503203
Size: 62.93 MB
Format: PDF
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Based on the authors’ lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems. Highlights Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form Classroom-tested and designed for students of mathematical statistics Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material Solutions provided for problems formulated at the end of each chapter Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models Theoretical, difficult, or frequently misunderstood problems are marked The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

Essentials Of Probability Theory For Statisticians

Author: Michael A. Proschan
Publisher: CRC Press
ISBN: 1498704204
Size: 62.62 MB
Format: PDF, ePub
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Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.

Elementary Applications Of Probability Theory Second Edition

Author: Henry C. Tuckwell
Publisher: CRC Press
ISBN: 9780412576201
Size: 36.26 MB
Format: PDF, Docs
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This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.

Introduction To Statistical Methods For Financial Models

Author: Thomas A Severini
Publisher: CRC Press
ISBN: 1351981900
Size: 63.86 MB
Format: PDF, Kindle
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This book provides an introduction to the use of statistical concepts and methods to model and analyze financial data. The ten chapters of the book fall naturally into three sections. Chapters 1 to 3 cover some basic concepts of finance, focusing on the properties of returns on an asset. Chapters 4 through 6 cover aspects of portfolio theory and the methods of estimation needed to implement that theory. The remainder of the book, Chapters 7 through 10, discusses several models for financial data, along with the implications of those models for portfolio theory and for understanding the properties of return data. The audience for the book is students majoring in Statistics and Economics as well as in quantitative fields such as Mathematics and Engineering. Readers are assumed to have some background in statistical methods along with courses in multivariate calculus and linear algebra.

Introduction To Statistical Limit Theory

Author: Alan M. Polansky
Publisher: CRC Press
ISBN: 1420076612
Size: 41.28 MB
Format: PDF, ePub, Docs
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Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field. The author explains as much of the background material as possible and offers a comprehensive account of the modes of convergence of random variables, distributions, and moments, establishing a firm foundation for the applications that appear later in the book. The text includes detailed proofs that follow a logical progression of the central inferences of each result. It also presents in-depth explanations of the results and identifies important tools and techniques. Through numerous illustrative examples, the book shows how asymptotic theory offers deep insight into statistical problems, such as confidence intervals, hypothesis tests, and estimation. With an array of exercises and experiments in each chapter, this classroom-tested book gives students the mathematical foundation needed to understand asymptotic theory. It covers the necessary introductory material as well as modern statistical applications, exploring how the underlying mathematical and statistical theories work together.

An Introduction To Statistical Inference And Its Applications With R

Author: Michael W. Trosset
Publisher: CRC Press
ISBN: 9781584889489
Size: 74.44 MB
Format: PDF, ePub, Docs
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Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures, and draw pseudorandom samples—not to perform entire analyses. After discussing the importance of chance in experimentation, the text develops basic tools of probability. The plug-in principle then provides a transition from populations to samples, motivating a variety of summary statistics and diagnostic techniques. The heart of the text is a careful exposition of point estimation, hypothesis testing, and confidence intervals. The author then explains procedures for 1- and 2-sample location problems, analysis of variance, goodness-of-fit, and correlation and regression. He concludes by discussing the role of simulation in modern statistical inference. Focusing on the assumptions that underlie popular statistical methods, this textbook explains how and why these methods are used to analyze experimental data.