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Probability: An Introduction
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 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.
A special feature is the authors' attention to rigorous 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.
288 pages, Paperback
First published November 20, 1986
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Displaying 1 - 2 of 2 reviews
March 23, 2021
The best single introduction to probability for first or second year undergraduate students, especially on courses similar to a typical UK undergraduate maths degree.
April 23, 2020
I've got the 2nd edition but not too much has changed. Too many probability books emphasise intuition at the expense of rigour. If you are like me your first course in probability had more to do with dice rolls, card games and interpretive dances than real math. Sigma-fields? Measurable spaces? Limit Theorems? Those are empty abstractions just getting in the way of understanding real statistics! right? Wrong.
Hand-waving away all the rigour to explain the higher level concepts might make students feel smart when 99% of the problems you are given involve at most two random variables but once you start to see random vectors, series convergences, measure theoretic probabilities, random processes and martingales thrown around like candy it becomes evidently clear that all that intuition matters little when trying to the chapter starts starts to feel more like you are deciphering hieroglyphics.
This is not a book for the enthusiastic beginner . This is an introductory Probability book for people who are going to be taking Statistics heavy courses until they graduate or move on to grad school. Although this book starts with sigma-fields and measures it isn't by any means Measure Theoretic, but it does build up a good foundation on the notion of probability spaces so you aren't left confused and stranded when your higher level courses and books start to make extensive references to such material.
This book doesn't waste time teaching you how to count or asking you to calculate numerous tail probabilities; it assumes you can figure that much out on your own. This is a book for people want a rigorous, mathematical and principled introduction to Probability.
Great book. Loved it.
Hand-waving away all the rigour to explain the higher level concepts might make students feel smart when 99% of the problems you are given involve at most two random variables but once you start to see random vectors, series convergences, measure theoretic probabilities, random processes and martingales thrown around like candy it becomes evidently clear that all that intuition matters little when trying to the chapter starts starts to feel more like you are deciphering hieroglyphics.
This is not a book for the enthusiastic beginner . This is an introductory Probability book for people who are going to be taking Statistics heavy courses until they graduate or move on to grad school. Although this book starts with sigma-fields and measures it isn't by any means Measure Theoretic, but it does build up a good foundation on the notion of probability spaces so you aren't left confused and stranded when your higher level courses and books start to make extensive references to such material.
This book doesn't waste time teaching you how to count or asking you to calculate numerous tail probabilities; it assumes you can figure that much out on your own. This is a book for people want a rigorous, mathematical and principled introduction to Probability.
Great book. Loved it.
Displaying 1 - 2 of 2 reviews