The aim of this book is to provide a straightforward introduction to the theory of probability. The topics covered illustrate the wide range and power of the subject, and include conditional probability, independence, random variables, generating functions, and an introduction to Markov chains. The text is friendly and clear and provides numerous worked examples and exercises, all of which help build up the important skills necessary for problem solving. The underlying probabilistic concepts are also well illustrated by this approach, making this book ideal both for self study and as a course text.
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Bryc W. This page intentionally left blank Elementary Probability 2nd Edition Now available in a fully revised and updated new edition, this well-established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacri? Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains.
This edition includes an elementary approach to martingales and the theory of Brownian motion, which supply the cornerstones for many topics in modern? The text is accessible to undergraduate students, and provides numerous worked examples and exercises to help build the important skills necessary for problem solving. This textbook can be recommended unreservedly.?
Internationale Mathematische Nachrichten? You may never need to buy another book on probability.? Keith Hirst, The Mathematical Gazette? A vast number of well-chosen worked examples and exercises guide the reader through the basic theory of probability at the elementary level. International Statistics Institute? A student with a solid background in calculus, linear algebra, and set theory will? Phil Gilbert, The Mathematics Teacher?
Stirzaker does an excellent job of developing problem-solving skills in an introductory probability text. Numerous examples and practice exercises are provided that only serve to enhance a student? Highly recommended.? Gougeon, Choice?
The book would make an excellent text for the properly prepared class, a solid instructor? Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published in print format ???? Contents Preface to the Second Edition page xi 0 Introduction 0. Exclusion 3. Recapture 5. Pairs of Dice 6. The Rejection Method 8. Death Process 9. Scholes Formula Problems Appendix: Solutions and Hints for Selected Exercises and Problems Further Reading Index of Notation Index Preface to the Second Edition The calculus of probabilities, in an appropriate form, should interest equally the mathematician, the experimentalist, and the statesman.
It is under its in? Francois Arago, Eulogy on Laplace, Lastly, one of the principal uses to which this Doctrine of Chances may be applied, is the discovering of some truths, which cannot fail of pleasing the mind, by their generality and simplicity; the admirable connexion of its consequences will increase the pleasure of the discovery; and the seeming paradoxes wherewith it abounds, will afford very great matter of surprize and entertainment to the inquisitive.
Abraham de Moivre, The Doctrine of Chances, This book provides an introduction to elementary probability and some of its simple applications. In particular, a principal purpose of the book is to help the student to solve problems.
Probability is now being taught to an ever wider audience, not all of whom can be assumed to have a high level of problem-solving skills and mathematical background. It is also characteristic of probability that, even at an elementary level, few problems are entirely routine. Successful problem solving requires?
Commonly, these skills are developed by observation of examples and practice at exercises, both of which this text aims to supply. With these targets in mind, in each chapter of the book, the theoretical exposition is accompanied by a large number of examples and is followed by worked examples incorporating a cluster of exercises. The examples and exercises have been chosen to illustrate the subject, to help the student solve the kind of problems typical of examinations, and for their entertainment value.
Besides its practical importance, probability is without doubt one of the most entertaining branches of mathematics. Each chapter concludes with problems: solutions to many of these appear in an appendix, together with the solutions to most of the exercises. The ordering and numbering of material in this second edition has for the most part been preserved from the? However, numerous alterations and additions have been included to make the basic material more accessible and the book more useful for self-study.
In xi xii Preface to the Second Edition particular, there is an entirely new introductory chapter that discusses our informal and intuitive ideas about probability, and explains how and why these should be incorporated into the theoretical framework of the rest of the book.
Also, all later chapters now include a section entitled,? Review and checklist,? Furthermore, a new section of the book provides a? Another new section provides an elementary introduction to Brownian motion, diffusion, and the Wiener process, which has underpinned much classical?
Scholes formula for pricing options. Optional stopping and its applications are introduced in the context of these important stochastic models, together with several associated new worked examples and exercises. The basic structure of the book remains unchanged; there are three main parts, each comprising three chapters.
It is assumed that the reader has some knowledge of elementary set theory. We adopt the now conventional formal de? This is not because of high principles, but merely because the alternative intuitive approach seems to lead more students into errors. The second part introduces discrete random variables, probability mass functions, and expectation.
It is assumed that the reader can do simple things with functions and series. The third part considers continuous random variables, and for this a knowledge of the simpler techniques of calculus is desirable. In addition, there are chapters on combinatorial methods in probability, the use of probability and other generating functions, and the basic theory of Markov processes in discrete and continuous time.
These sections can be omitted at a? In general, the material is presented in a conventional order, which roughly corresponds to increasing levels of knowledge and dexterity on the part of the reader.
Those who start with a suf? For example, you may want to read Chapters 4 and 7 together and then Chapters 5 and 8 together , regarding discrete and continuous random variables as two varieties of the same species which they are.
Also, much of Chapter 9 could be read immediately after Chapter 5, if you prefer. In particular, the book is structured so that the? This layout entails some repetition of similar ideas in different contexts, and this should help to reinforce the reader? The ends of examples, proofs, and de? Finally, you should note that the book contains a random number of errors. I entreat readers to inform me of all those they? Oxford, January 0 Introduction A life which included no improbable events would be the real statistical improbability.
Poul Anderson It is plain that any scientist is trying to correlate the incoherent body of facts confronting him with some de? Hardy This chapter introduces the basic concepts of probability in an informal way.
We discuss our everyday experience of chance, and explain why we need a theory and how we start to construct one. Mathematical probability is motivated by our intuitive ideas about likelihood as a proportion in many practical instances. We discuss some of the more common questions and problems in probability, and conclude with a brief account of the history of the subject.
Even then, there is always the chance that you will fall out. Robert Benchley It is not certain that everything is uncertain. Blaise Pascal You can be reasonably con? In fact, the one thing we can be certain of is that uncertainty and randomness are unavoidable aspects of our experience. At a personal level, minor ailments and diseases appear unpredictably and are resolved not much more predictably. Your income and spending are subject to erratic strokes of good or bad fortune.
Your genetic makeup is a random selection from those of your parents. The weather is notoriously? You may decide to play 1 2 0 Introduction cards, invest in shares, bet on horses, buy lottery tickets, or engage in one or several other forms of gambling on events that are necessarily uncertain otherwise, gambling could not occur.
At a different level, society has to organize itself in the context of similar sorts of uncertainty. Engineers have to build structures to withstand stressful events of unknown magnitude and frequency. Computing and communication systems need to be designed to cope with uncertain and? Any system should be designed to have a small chance of failing and a high chance of performing as it was intended.
Financial markets of any kind should function so as to share out risks in an ef? This uncertainty is not con? Of course, our ignorance of the past is perhaps not quite as pressing as our ignorance of the future because of the direction in which time? But the arguments about the past are, paradoxically, somewhat more bad tempered as a rule. In addition, and maybe most annoyingly, we are not certain about events occurring right now, even among those within our direct observation.
At a serious level, you can see the human genome expressing itself in everyone you know, but the mechanisms remain largely a mystery. The task of unravelling this genetic conundrum will require a great deal of probability theory and statistical analysis. At a more trivial level, illusionists and politicians make a handsome living from our dif?
It follows that everyone must have some internal concept of chance to live in the real world, although such ideas may be implicit or even unacknowledged. These concepts of chance have long been incorporated into many cultures in mythological or religious form. The casting of lots sortilege to make choices at random is widespread; we are all familiar with?
The Romans, for example, had gods of chance named Fortuna and Fors, and even today we have Lady Luck. Note that if you ransack the archives of the literary response to this state of affairs, one?
ISBN 13: 9780521421836