Ross%20s[1][1].%20introduction%20to%20probability%20models%20%289ed.%2c%20ap%2c%202007%29%28is

Ross%20S[1][1].%20Introduction%20to%20probability%20models%20%289ed.%2C%20AP%2C%202007%29%28IS
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Unformatted text preview: Introduction to Probability Models Ninth Edition This page intentionally left blank Introduction to Probability Models Ninth Edition Sheldon M. Ross University of California Berkeley, California AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an imprint of Elsevier Acquisitions Editor Tom Singer Project Manager Sarah M. Hajduk Marketing Managers Linda Beattie, Leah Ackerson Cover Design Eric DeCicco Composition VTEX Cover Printer Phoenix Color Interior Printer The Maple-Vail Book Manufacturing Group Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobalds Road, London WC1X 8RR, UK This book is printed on acid-free paper. ° Copyright © 2007, Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elseviers Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.com. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting Support & Contact then Copyright and Permission and then Obtaining Permissions. Library of Congress Cataloging-in-Publication Data Application Submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN-13: 978-0-12-598062-3 ISBN-10: 0-12-598062-0 For information on all Academic Press publications visit our Web site at www.books.elsevier.com Printed in the United States of America 06 07 08 09 10 9 8 7 6 5 4 3 2 1 Contents Preface xiii 1. Introduction to Probability Theory 1 1.1. Introduction 1 1.2. Sample Space and Events 1 1.3. Probabilities Defined on Events 4 1.4. Conditional Probabilities 7 1.5. Independent Events 10 1.6. Bayes Formula 12 Exercises 15 References 21 2. Random Variables 23 2.1. Random Variables 23 2.2. Discrete Random Variables 27 2.2.1. The Bernoulli Random Variable 28 2.2.2. The Binomial Random Variable 29 2.2.3. The Geometric Random Variable 31 2.2.4. The Poisson Random Variable 32 2.3. Continuous Random Variables 34 2.3.1. The Uniform Random Variable 35 2.3.2. Exponential Random Variables 36 2.3.3. Gamma Random Variables 37 2.3.4. Normal Random Variables 37 v vi Contents 2.4. Expectation of a Random Variable 38 2.4.1. The Discrete Case 38 2.4.2. The Continuous Case 41 2.4.3. Expectation of a Function of a Random Variable 43 2.5. Jointly Distributed Random Variables 47 2.5.1. Joint Distribution Functions 47 2.5.2. Independent Random Variables 51 2.5.3. Covariance and Variance of Sums of Random Variables 53 2....
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