## A Course in Probability

**Author**: Neil A. Weiss,Paul T. Holmes,Michael Hardy

**Publisher:**Pearson College Division

**ISBN:**9780201774719

**Category:**Mathematics

**Page:**789

**View:**2040

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This text is intended primarily for readers interested in mathematical probability as applied to mathematics, statistics, operations research, engineering, and computer science. It is also appropriate for mathematically oriented readers in the physical and social sciences. Prerequisite material consists of basic set theory and a firm foundation in elementary calculus, including infinite series, partial differentiation, and multiple integration. Some exposure to rudimentary linear algebra (e.g., matrices and determinants) is also desirable. This text includes pedagogical techniques not often found in books at this level, in order to make the learning process smooth, efficient, and enjoyable. Fundamentals of Probability: Probability Basics. Mathematical Probability. Combinatorial Probability. Conditional Probability and Independence.Discrete Random Variables: Discrete Random Variables and Their Distributions. Jointly Discrete Random Variables. Expected Value of Discrete Random Variables.Continuous Random Variables: Continuous Random Variables and Their Distributions. Jointly Continuous Random Variables. Expected Value of Continuous Random Variables.Limit Theorems and Advanced Topics: Generating Functions and Limit Theorems. Additional Topics. For all readers interested in probability.

## A Course in Probability Theory

**Author**: Kai Lai Chung

**Publisher:**Academic Press

**ISBN:**0080570402

**Category:**Mathematics

**Page:**365

**View:**2276

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This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

## A First Course in Probability

**Author**: Sheldon M. Ross

**Publisher:**Pearson College Division

**ISBN:**9780321794772

**Category:**Mathematics

**Page:**467

**View:**2387

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A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.

## Weighing the Odds

*A Course in Probability and Statistics*

**Author**: David Williams

**Publisher:**Cambridge University Press

**ISBN:**9780521006187

**Category:**Mathematics

**Page:**547

**View:**9091

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Advanced textbook; many examples and exercises, often with hints or solutions; code provided for computational examples and simulations.

## A Course in Probability and Statistics

**Author**: Charles Joel Stone

**Publisher:**Cengage Learning

**ISBN:**N.A

**Category:**Mathematics

**Page:**838

**View:**585

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This author's modern approach is intended primarily for honors undergraduates or undergraduates with a good math background taking a mathematical statistics or statistical inference course. The author takes a finite-dimensional functional modeling viewpoint (in contrast to the conventional parametric approach) to strengthen the connection between statistical theory and statistical methodology.

## An Intermediate Course in Probability

**Author**: Allan Gut

**Publisher:**Springer Science & Business Media

**ISBN:**1441901620

**Category:**Mathematics

**Page:**303

**View:**1557

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This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.

## First Course in Probability, A: Pearson New International Edition

**Author**: Sheldon Ross

**Publisher:**Pearson Higher Ed

**ISBN:**1292037563

**Category:**Mathematics

**Page:**464

**View:**1531

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A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.

## A Basic Course in Probability Theory

**Author**: Rabi Bhattacharya,Edward C. Waymire

**Publisher:**Springer

**ISBN:**3319479741

**Category:**Mathematics

**Page:**265

**View:**782

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This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

## A Graduate Course in Probability

**Author**: Howard G. Tucker

**Publisher:**Academic Press

**ISBN:**1483220508

**Category:**Mathematics

**Page:**288

**View:**5151

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Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini's theorem, Radon-Nikodym theorem, Egorov's theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work.

## e-Study Guide for: A Course in Probability Theory, Revised Edition by Kai Lai Chung, ISBN 9780121741518

**Author**: Cram101 Textbook Reviews

**Publisher:**Cram101 Textbook Reviews

**ISBN:**1467213209

**Category:**Education

**Page:**24

**View:**6776

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Never Highlight a Book Again! Just the FACTS101 study guides give the student the textbook outlines, highlights, practice quizzes and optional access to the full practice tests for their textbook.

## Elementary Probability Theory with Stochastic Processes

**Author**: K. L. Chung

**Publisher:**Springer Science & Business Media

**ISBN:**1475751141

**Category:**Mathematics

**Page:**325

**View:**3263

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In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.

## A First Course in Probability and Markov Chains

**Author**: Giuseppe Modica,Laura Poggiolini

**Publisher:**John Wiley & Sons

**ISBN:**111847774X

**Category:**Mathematics

**Page:**352

**View:**4005

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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.

## A Course in Mathematical Statistics

**Author**: George G. Roussas

**Publisher:**Elsevier

**ISBN:**0080493149

**Category:**Mathematics

**Page:**572

**View:**1929

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A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference. * Contains 25% new material * Includes the most complete coverage of sufficiency * Transformation of Random Vectors * Sufficiency / Completeness / Exponential Families * Order Statistics * Elements of Nonparametric Density Estimation * Analysis of Variance (ANOVA) * Regression Analysis * Linear Models

## Probability Theory

*A First Course in Probability Theory and Statistics*

**Author**: Werner Linde

**Publisher:**Walter de Gruyter GmbH & Co KG

**ISBN:**3110466198

**Category:**Mathematics

**Page:**409

**View:**3961

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This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Mathematical Statistics Appendix Bibliography Index

## Introduction to Probability Models

**Author**: Sheldon M. Ross

**Publisher:**Elsevier

**ISBN:**1483276589

**Category:**Mathematics

**Page:**568

**View:**1311

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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.

## Problems in Probability

**Author**: Albert N. Shiryaev

**Publisher:**Springer Science & Business Media

**ISBN:**1461436885

**Category:**Mathematics

**Page:**428

**View:**6511

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For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students. Many of the exercises included in the book contain helpful hints and other relevant information. Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book. This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.

## Basic Probability Theory with Applications

**Author**: Mario Lefebvre

**Publisher:**Springer Science & Business Media

**ISBN:**0387749950

**Category:**Mathematics

**Page:**340

**View:**1132

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The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering. Chapters 2 to 4 cover the probability theory they generally need in their training. Although the treatment of the subject is surely su?cient for non-mathematicians, I intentionally avoided getting too much into detail. For instance, topics such as mixed type random variables and the Dirac delta function are only brie?y mentioned. Courses on probability theory are often considered di?cult. However, after having taught this subject for many years, I have come to the conclusion that one of the biggest problems that the students face when they try to learn probability theory, particularly nowadays, is their de?ciencies in basic di?erential and integral calculus. Integration by parts, for example, is often already forgotten by the students when they take a course on probability. For this reason, I have decided to write a chapter reviewing the basic elements of di?erential calculus. Even though this chapter might not be covered in class, the students can refer to it when needed. In this chapter, an e?ort was made to give the readers a good idea of the use in probability theory of the concepts they should already know. Chapter 2 presents the main results of what is known as elementary probability, including Bayes’ rule and elements of combinatorial analysis.

## A First Course in Probability

**Author**: Tapas K. Chandra,Dipak Chatterjee

**Publisher:**Alpha Science Int'l Ltd.

**ISBN:**9781842652084

**Category:**Business & Economics

**Page:**494

**View:**4977

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Covers topics such as transformation, convergence and multivariate analysis. This book offers a feature that resolve many confusions of probability and statistics.

## A Basic Course in Measure and Probability

*Theory for Applications*

**Author**: Ross Leadbetter,Stamatis Cambanis,Vladas Pipiras

**Publisher:**Cambridge University Press

**ISBN:**1107020409

**Category:**Mathematics

**Page:**376

**View:**6594

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A concise introduction covering all of the measure theory and probability most useful for statisticians.

## Introduction to Probability and Statistics for Engineers and Scientists

**Author**: Sheldon M. Ross

**Publisher:**Academic Press

**ISBN:**0123948428

**Category:**Mathematics

**Page:**686

**View:**1228

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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.