FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS

T.T. Soong State University of New York at Buffalo, Buffalo, New York, USA

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TLFeBOOK

FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS

TLFeBOOK

TLFeBOOK

FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS

T.T. Soong State University of New York at Buffalo, Buffalo, New York, USA

TLFeBOOK

Copyright 2004

John Wiley & Sons Ltd, The Atrium, Southern G ate, Chichester, West Sussex PO19 8SQ, England Telephone ( 44) 1243 779777

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British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-86813-9 (Cloth) ISBN 0-470-86814-7 (Paper) Typeset in 10/12pt Times from LaTeX files supplied by the author, processed by Integra Software Services, Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by Biddles Ltd, Guildford, Surrey This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

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To the memory of my parents

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Contents

PREFACE 1 INTRODUCTION 1.1 Organization of Text 1.2 Probability Tables and Computer Software 1.3 Prerequisites PART A: PROBABILITY AND RANDOM VARIABLES 2 BASIC PROBABILITY CONCEPTS 2.1 Elements of Set Theory 2.1.1 Set Operations 2.2 Sample Space and Probability Measure 2.2.1 Axioms of Probability 2.2.2 Assignment of Probability 2.3 Statistical Independence 2.4 Conditional Probability R eference F urther R eading Problems 3 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 3.1 R andom Variables 3.2 Probability Distributions 3.2.1 Probability D istribution F unction 3.2.2 Probability M ass F unction for D iscrete R andom Variables xiii 1 2 3 3 5 7 8 9 12 13 16 17 20 28 28 28

37 37 39 39 41

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viii 3.2.3 Probability D ensity F unction for Continuous R andom Variables 3.2.4 M ixed-Type D istribution 3.3 Two or M ore R andom Variables 3.3.1 Joint Probability D istribution F unction 3.3.2 Joint Probability Mass F unction 3.3.3 Joint Probability Density F unction 3.4...