Probability via Expectation

This book is a complete revision of the earlier work Probability which ap­ peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim w

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Continued at end of book

Peter Whittle

Probability via Expectation Third Edition

With 22 Illustrations

Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest

Peter Whittle Department of Pure Mathematics and Mathematical Statistics University of Cambridge 16 Mill Lane Cambridge CB2 ISB England

Editorial Board Stephen Fienberg York University North York, Ontario M3J IP3 Canada

Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305 USA

Mathematics Subject Classification: 60-01 First edition, Penguin 1970.

Second edition, Wiley, 1976

Russian translation, Nakua, 1982.

Whittle, Peter. Probability via expectation I by Peter Whittle. - 3rd ed. p. cm. - (Springer texts in statistics) Rev. ed. of Probability. 1976. Includes bibliographical references and index. ISBN·I3: 978·0·387·97764·5 DOl: 10.10071978·1·4612·2892·9

e·ISBN·I3: 978·1·4612·2892·9

1. Probabilities. I. Whittle, Peter. Probability. II. Title. ill. Series.

QA273.W59 1992 519.2-dc 20

91-40782

Printed on acid·free paper.

© 1992 Springer·Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer·Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA) except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production coordinated by Brian Howe and managed by Terry Kornak; manufacturing supervised by Jacqui Ashri. Typ