Basic Probability Theory

Author : Mario Lefebvre
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 47,5 Mb
Release : 2009-10-03
Category : Mathematics
ISBN : 9780387749952

Get Book

Basic Probability Theory with Applications by Mario Lefebvre Pdf

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.

Author : Robert B. Ash
Publisher : Courier Corporation
Page : 354 pages
File Size : 45,5 Mb
Release : 2008-06-26
Category : Mathematics
ISBN : 9780486466286

Get Book

Basic Probability Theory by Robert B. Ash Pdf

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.

Author : Rabi Bhattacharya,Edward C. Waymire
Publisher : Springer
Page : 265 pages
File Size : 55,5 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319479743

Get Book

A Basic Course in Probability Theory by Rabi Bhattacharya,Edward C. Waymire Pdf

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.

Author : Henry C. Tuckwell
Publisher : CRC Press
Page : 308 pages
File Size : 46,5 Mb
Release : 2018-02-06
Category : Mathematics
ISBN : 9781351452960

Get Book

Elementary Applications of Probability Theory by Henry C. Tuckwell Pdf

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.

Author : K. L. Chung
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 46,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739732

Get Book

Elementary Probability Theory with Stochastic Processes by K. L. Chung Pdf

This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.

Author : Valeriy Skorokhod
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 42,6 Mb
Release : 2005-12-05
Category : Mathematics
ISBN : 9783540263128

Get Book

Basic Principles and Applications of Probability Theory by Valeriy Skorokhod Pdf

The book is an introduction to modern probability theory written by one of the famous experts in this area. Readers will learn about the basic concepts of probability and its applications, preparing them for more advanced and specialized works.

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 47,6 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

Get Book

Probability by Rick Durrett Pdf

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Author : Boris Vladimirovich Gnedenko,Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 162 pages
File Size : 47,8 Mb
Release : 1962-01-01
Category : Mathematics
ISBN : 9780486601557

Get Book

An Elementary Introduction to the Theory of Probability by Boris Vladimirovich Gnedenko,Aleksandr I?Akovlevich Khinchin Pdf

This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

Author : Charles Miller Grinstead,James Laurie Snell
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 41,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0821807498

Get Book

Introduction to Probability by Charles Miller Grinstead,James Laurie Snell Pdf

This text is designed for an introductory probability course at the university level for undergraduates in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a firm understanding of the subject.

Author : Edward Nelson
Publisher : Princeton University Press
Page : 107 pages
File Size : 44,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882144

Get Book

Radically Elementary Probability Theory. (AM-117), Volume 117 by Edward Nelson Pdf

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Author : Paul E. Pfeiffer
Publisher : Courier Corporation
Page : 416 pages
File Size : 45,5 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486165660

Get Book

Concepts of Probability Theory by Paul E. Pfeiffer Pdf

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Author : Michael H. Herzog,Gregory Francis,Aaron Clarke
Publisher : Springer
Page : 146 pages
File Size : 47,8 Mb
Release : 2019-08-13
Category : Science
ISBN : 9783030034993

Get Book

Understanding Statistics and Experimental Design by Michael H. Herzog,Gregory Francis,Aaron Clarke Pdf

This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.

Author : M. Loeve
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 45,7 Mb
Release : 1977-03-29
Category : Mathematics
ISBN : 0387902104

Get Book

Probability Theory I by M. Loeve Pdf

This fourth edition contains several additions. The main ones con cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Proba bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduc tion, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independ ence which played and continues to playa central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attrac tion completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions.

Author : Ash
Publisher : Unknown
Page : 128 pages
File Size : 44,6 Mb
Release : 1970-01-01
Category : Electronic
ISBN : 047103455X

Get Book

Solutions Basic Probability Theory by Ash Pdf

Author : I︠U︡riĭ Vasilʹevich Prokhorov,I͡Uriĭ Anatolʹevich Rozanov
Publisher : Springer
Page : 434 pages
File Size : 48,7 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015038846005

Get Book

Probability Theory by I︠U︡riĭ Vasilʹevich Prokhorov,I͡Uriĭ Anatolʹevich Rozanov Pdf