Exercises In Probability

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Exercises in Probability

T. Cacoullos
Exercises in Probability Book PDF

Author : T. Cacoullos
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461245261

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Exercises in Probability by T. Cacoullos Pdf

The author, the founder of the Greek Statistical Institute, has based this book on the two volumes of his Greek edition which has been used by over ten thousand students during the past fifteen years. It can serve as a companion text for an introductory or intermediate level probability course. Those will benefit most who have a good grasp of calculus, yet, many others, with less formal mathematical background can also benefit from the large variety of solved problems ranging from classical combinatorial problems to limit theorems and the law of iterated logarithms. It contains 329 problems with solutions as well as an addendum of over 160 exercises and certain complements of theory and problems.

One Thousand Exercises in Probability

Geoffrey Grimmett,David Stirzaker
One Thousand Exercises in Probability Book PDF

Author : Geoffrey Grimmett,David Stirzaker
Publisher : Oxford University Press
Page : 452 pages
File Size : 50,5 Mb
Release : 2001-05-24
Category : Business & Economics
ISBN : 0198572212

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One Thousand Exercises in Probability by Geoffrey Grimmett,David Stirzaker Pdf

This guide provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution. Topics include modelling and many applications of probability theory.

Exercises in Probability

Loïc Chaumont,Marc Yor
Exercises in Probability Book PDF

Author : Loïc Chaumont,Marc Yor
Publisher : Cambridge University Press
Page : 301 pages
File Size : 47,7 Mb
Release : 2012-07-19
Category : Mathematics
ISBN : 9781107606555

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Exercises in Probability by Loïc Chaumont,Marc Yor Pdf

Over 100 exercises with detailed solutions, insightful notes and references for further reading. Ideal for beginning researchers.

Exercises in Probability

L. Chaumont,M. Yor
Exercises in Probability Book PDF

Author : L. Chaumont,M. Yor
Publisher : Cambridge University Press
Page : 256 pages
File Size : 48,9 Mb
Release : 2003-11-03
Category : Mathematics
ISBN : 9780521825856

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Exercises in Probability by L. Chaumont,M. Yor Pdf

This book was first published in 2003. Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning, Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.

One Thousand Exercises in Probability

Geoffrey Grimmett,David Stirzaker
One Thousand Exercises in Probability Book PDF

Author : Geoffrey Grimmett,David Stirzaker
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 53,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9780198847618

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One Thousand Exercises in Probability by Geoffrey Grimmett,David Stirzaker Pdf

This third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence, stationary processes, renewals, queues, martingales, diffusions, L�vy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance. The text is intended to serve students as a companion for elementary, intermediate, and advanced courses in probability, random processes and operations research. It will also be useful for anyone needing a source for large numbers of problems and questions in these fields. In particular, this book acts as a companion to the authors' volume, Probability and Random Processes, fourth edition (OUP 2020).

Introduction to Probability

Joseph K. Blitzstein,Jessica Hwang
Introduction to Probability Book PDF

Author : Joseph K. Blitzstein,Jessica Hwang
Publisher : CRC Press
Page : 599 pages
File Size : 49,5 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781466575578

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Introduction to Probability by Joseph K. Blitzstein,Jessica Hwang Pdf

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.

One Thousand Exercises in Probability

Geoffrey Grimmett,David Stirzaker
One Thousand Exercises in Probability Book PDF

Author : Geoffrey Grimmett,David Stirzaker
Publisher : Oxford University Press
Page : 480 pages
File Size : 54,7 Mb
Release : 2020-07-03
Category : Mathematics
ISBN : 9780192586872

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One Thousand Exercises in Probability by Geoffrey Grimmett,David Stirzaker Pdf

This third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence, stationary processes, renewals, queues, martingales, diffusions, Lévy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance. The text is intended to serve students as a companion for elementary, intermediate, and advanced courses in probability, random processes and operations research. It will also be useful for anyone needing a source for large numbers of problems and questions in these fields. In particular, this book acts as a companion to the authors' volume, Probability and Random Processes, fourth edition (OUP 2020).

A First Look at Rigorous Probability Theory

Jeffrey Seth Rosenthal
A First Look at Rigorous Probability Theory Book PDF

Author : Jeffrey Seth Rosenthal
Publisher : World Scientific
Page : 238 pages
File Size : 51,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812703705

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A First Look at Rigorous Probability Theory by Jeffrey Seth Rosenthal Pdf

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.

Applied Probability

Kenneth Lange
Applied Probability Book PDF

Author : Kenneth Lange
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 46,7 Mb
Release : 2008-01-17
Category : Mathematics
ISBN : 9780387227115

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Applied Probability by Kenneth Lange Pdf

Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

Problems in Probability

Albert N. Shiryaev
Problems in Probability Book PDF

Author : Albert N. Shiryaev
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 42,9 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9781461436881

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Problems in Probability by Albert N. Shiryaev Pdf

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.

Probability

Rick Durrett
Probability Book PDF

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,5 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

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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.

Probability and Bayesian Modeling

Jim Albert,Jingchen Hu
Probability and Bayesian Modeling Book PDF

Author : Jim Albert,Jingchen Hu
Publisher : CRC Press
Page : 553 pages
File Size : 43,7 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9781351030137

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Probability and Bayesian Modeling by Jim Albert,Jingchen Hu Pdf

Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Probability

Davar Khoshnevisan
Probability Book PDF

Author : Davar Khoshnevisan
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 53,6 Mb
Release : 2007
Category : Probabilities
ISBN : 9780821842157

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Probability by Davar Khoshnevisan Pdf

This is a textbook for a one-semester graduate course in measure-theoretic probability theory, but with ample material to cover an ordinary year-long course at a more leisurely pace. Khoshnevisan's approach is to develop the ideas that are absolutely central to modern probability theory, and to showcase them by presenting their various applications. As a result, a few of the familiar topics are replaced by interesting non-standard ones. The topics range from undergraduate probability and classical limit theorems to Brownian motion and elements of stochastic calculus. Throughout, the reader will find many exciting applications of probability theory and probabilistic reasoning. There are numerous exercises, ranging from the routine to the very difficult. Each chapter concludes with historical notes.

Fifty Challenging Problems in Probability with Solutions

Frederick Mosteller
Fifty Challenging Problems in Probability with Solutions Book PDF

Author : Frederick Mosteller
Publisher : Courier Corporation
Page : 88 pages
File Size : 45,6 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486134963

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Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller Pdf

Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions.

Introduction to Probability

Charles Miller Grinstead,James Laurie Snell
Introduction to Probability Book PDF

Author : Charles Miller Grinstead,James Laurie Snell
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 45,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0821807498

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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.