Basic Probability Theory With Applications Download Ebook PDF Epub Online

Author : Mario Lefebvre
Publisher : Springer Science & Business Media
Release : 2009-10-03
Page : 340
Category : Mathematics
ISBN 13 : 0387749950
Description :


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 : Larry Rabinowitz
Publisher : CRC Press
Release : 2016-11-03
Page : 218
Category : Mathematics
ISBN 13 : 1498771343
Description :


Elementary Probability with Applications, Second Edition shows students how probability has practical uses in many different fields, such as business, politics, and sports. In the book, students learn about probability concepts from real-world examples rather than theory. The text explains how probability models with underlying assumptions are used to model actual situations. It contains examples of probability models as they relate to: Bloc voting Population genetics Doubling strategies in casinos Machine reliability Airline management Cryptology Blood testing Dogs resembling owners Drug detection Jury verdicts Coincidences Number of concert hall aisles 2000 U.S. presidential election Points after deuce in tennis Tests regarding intelligent dogs Music composition Based on the author’s course at The College of William and Mary, the text can be used in a one-semester or one-quarter course in discrete probability with a strong emphasis on applications. By studying the book, students will appreciate the subject of probability and its applications and develop their problem-solving and reasoning skills.


Author : Henry C. Tuckwell
Publisher : Routledge
Release : 2018-02-06
Page : 308
Category : Mathematics
ISBN 13 : 1351452959
Description :


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 : Robert B. Ash
Publisher : Courier Corporation
Release : 2008-06-26
Page : 337
Category : Mathematics
ISBN 13 : 0486466280
Description :


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 : Ross Leadbetter
Stamatis Cambanis
Publisher : Cambridge University Press
Release : 2014-01-30
Page : 376
Category : Mathematics
ISBN 13 : 1107020409
Description :


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


Author : Malempati M. Rao
Randall J. Swift
Publisher : Springer Science & Business Media
Release : 2006-03-15
Page : 530
Category : Mathematics
ISBN 13 : 0387277307
Description :


This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications. The new edition offers a detailed treatment of the core area of probability, and both structural and limit results are presented in detail. Compared to the first edition, the material and presentation are better highlighted; each chapter is improved and updated.


Author : Géza Schay
Publisher : Birkhäuser
Release : 2016-06-17
Page : 385
Category : Mathematics
ISBN 13 : 3319306200
Description :


Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises“/p> Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. ... the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ ... Each new concept is clearly explained and is followed by many detailed examples. ... numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)


Author : Gunnar Blom
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 356
Category : Mathematics
ISBN 13 : 1461235669
Description :


This is a somewhat extended and modified translation of the third edition of the text, first published in 1969. The Swedish edition has been used for many years at the Royal Institute of Technology in Stockholm, and at the School of Engineering at Link6ping University. It is also used in elementary courses for students of mathematics and science. The book is not intended for students interested only in theory, nor is it suited for those seeking only statistical recipes. Indeed, it is designed to be intermediate between these extremes. I have given much thought to the question of dividing the space, in an appropriate way, between mathematical arguments and practical applications. Mathematical niceties have been left aside entirely, and many results are obtained by analogy. The students I have in mind should have three ingredients in their course: elementary probability theory with applications, statistical theory with applications, and something about the planning of practical investiga tions. When pouring these three ingredients into the soup, I have tried to draw upon my experience as a university teacher and on my earlier years as an industrial statistician. The programme may sound bold, and the reader should not expect too much from this book. Today, probability, statistics and the planning of investigations cover vast areas and, in 356 pages, only the most basic problems can be discussed. If the reader gains a good understanding of probabilistic and statistical reasoning, the main purpose of the book has been fulfilled.


Author : Melvin Hausner
Publisher : Springer
Release : 2013-12-11
Page : 310
Category : Mathematics
ISBN 13 : 9781461357063
Description :


This text contains ample material for a one term precalculus introduction to probability theory. lt can be used by itself as an elementary introduc tion to probability, or as the probability half of a one-year probability statistics course. Although the development of the subject is rigorous, experimental motivation is maintained throughout the text. Also, statistical and practical applications are given throughout. The core of the text consists of the unstarred sections, most of chapters 1-3 and 5-7. Included are finite probability spaces, com binatorics, set theory, independence and conditional probability, random variables, Chebyshev's theorem, the law of large numbers, the binomial distribution, the normal distribution and the normal approxi mation to the binomial distribution. The starred sections include limiting and infinite processes, a mathematical discussion of symmetry, and game theory. These sections are indicated with an*, and are optional and sometimes more difficult. I have, in most places throughout the text, given decimal equivalents to fractional answers. Thus, while the mathematician finds the answer p = 17/143 satisfactory, the scientist is best appeased by the decimal approximation p = 0.119. A decimal answer gives a ready way of find ing the correct order of magnitude and of comparing probabilities.


Author : K. L. Chung
Publisher : Springer Science & Business Media
Release : 2013-03-09
Page : 325
Category : Mathematics
ISBN 13 : 1475751141
Description :


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.


Author : Valeriy Skorokhod
Publisher : Springer Science & Business Media
Release : 2005-12-05
Page : 282
Category : Mathematics
ISBN 13 : 9783540263128
Description :


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 : Jeffrey Seth Rosenthal
Publisher : World Scientific
Release : 2006
Page : 219
Category : Mathematics
ISBN 13 : 9812703705
Description :


Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.


Author : Enders A. Robinson
Publisher : Springer Science & Business Media
Release : 2013-12-11
Page : 420
Category : Mathematics
ISBN 13 : 9400953860
Description :


Probability theory and its applications represent a discipline of fun damental importance to nearly all people working in the high-tech nology world that surrounds us. There is increasing awareness that we should ask not "Is it so?" but rather "What is the probability that it is so?" As a result, most colleges and universities require a course in mathematical probability to be given as part of the undergraduate training of all scientists, engineers, and mathematicians. This book is a text for a first course in the mathematical theory of probability for undergraduate students who have the prerequisite of at least two, and better three, semesters of calculus. In particular, the student must have a good working knowledge of power series expan sions and integration. Moreover, it would be helpful if the student has had some previous exposure to elementary probability theory, either in an elementary statistics course or a finite mathematics course in high school or college. If these prerequisites are met, then a good part of the material in this book can be covered in a semester (IS-week) course that meets three hours a week.


Author : Liliana Blanco Castañeda
Viswanathan Arunachalam
Publisher : John Wiley & Sons
Release : 2014-08-21
Page : 614
Category : Mathematics
ISBN 13 : 1118344960
Description :


An easily accessible, real-world approach to probability andstochastic processes Introduction to Probability and Stochastic Processes withApplications presents a clear, easy-to-understand treatment ofprobability and stochastic processes, providing readers with asolid foundation they can build upon throughout their careers. Withan emphasis on applications in engineering, applied sciences,business and finance, statistics, mathematics, and operationsresearch, the book features numerous real-world examples thatillustrate how random phenomena occur in nature and how to useprobabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basicconcepts of probability to advanced topics for further study,including Itô integrals, martingales, and sigma algebras.Additional topical coverage includes: Distributions of discrete and continuous random variablesfrequently used in applications Random vectors, conditional probability, expectation, andmultivariate normal distributions The laws of large numbers, limit theorems, and convergence ofsequences of random variables Stochastic processes and related applications, particularly inqueueing systems Financial mathematics, including pricing methods such asrisk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisitemathematics and tables of standard distributions for use inapplications are provided, and plentiful exercises, problems, andsolutions are found throughout. Also, a related website featuresadditional exercises with solutions and supplementary material forclassroom use. Introduction to Probability and StochasticProcesses with Applications is an ideal book for probabilitycourses at the upper-undergraduate level. The book is also avaluable reference for researchers and practitioners in the fieldsof engineering, operations research, and computer science whoconduct data analysis to make decisions in their everyday work.


Author : Rabi Bhattacharya
Edward C. Waymire
Publisher : Springer
Release : 2017-02-13
Page : 265
Category : Mathematics
ISBN 13 : 3319479741
Description :


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 : Roman Vershynin
Publisher : Cambridge University Press
Release : 2018-09-27
Page : 296
Category : Business & Economics
ISBN 13 : 1108415199
Description :


An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.


Author : Rick Durrett
Publisher : Cambridge University Press
Release : 2009-07-31
Page :
Category : Mathematics
ISBN 13 : 1139480731
Description :


This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.


Author : Oliver Knill
Publisher : World Scientific Publishing Company
Release : 2017-01-31
Page : 500
Category : Mathematics
ISBN 13 : 9789813109490
Description :


This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.


Author : Y. A. Rozanov
Publisher : Courier Corporation
Release : 2013-05-27
Page : 148
Category : Mathematics
ISBN 13 : 0486321142
Description :


This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.


Author : Krishna B. Athreya
Soumendra N. Lahiri
Publisher : Springer Science & Business Media
Release : 2006-11-24
Page : 619
Category : Mathematics
ISBN 13 : 0387354344
Description :


This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics.