One Thousand Exercises In Probability

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.

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).

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.

This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions.

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

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).

Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.

Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

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.