Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống
1
/ 408 trang
THÔNG TIN TÀI LIỆU
Thông tin cơ bản
Định dạng
Số trang
408
Dung lượng
5,25 MB
Nội dung
TLFeBOOK
FUNDAMENTALS OF PROBABILITY
AND STATISTICSFOR ENGINEERS
T. T. Soong
State University of New York at Buffalo, Buffalo, New York, USA
TLFeBOOK
TLFeBOOK
FUNDAMENTALS OF
PROBABILITY AND
STATISTICS FOR
ENGINEERS
TLFeBOOK
TLFeBOOK
FUNDAMENTALS OF PROBABILITY
AND STATISTICSFOR 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
Email (for orders and customer service enquiries): cs-books@wiley.co.uk
Visit our Home Page on www.wileyeurope.com or www.wiley.com
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording, scanning or otherwise, except under the terms of the Copyright, Designs and
Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency
Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of
the Publisher. Requests to the Publisher should be addressed to the Permissions Department,
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ,
England, or emailed to permreq@wiley.co.uk, or faxed to ( 44) 1243 770620.
This publication is designed to provide accurate and authoritative information in regard to
the subject matter covered. It is sold on the understanding that the Publisher is not engaged in
rendering professional services. If professional advice or other expert assistance is required,
the services of a competent professional should be sought.
Other W iley Editorial Offices
John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, U SA
Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA
Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany
John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia
John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark,
Singapore 129809
John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1
Wiley also publishes its books in a variety of electronic formats. Some content that appears
in print may not be available in electronic books.
British Library Ca taloguing 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.
TLFeBOOK
To the memory of my parents
TLFeBOOK
TLFeBOOK
Contents
PREFACE xiii
1 INTRODUCTION 1
1.1 Organization of Text 2
1.2 Probability Tables and Computer Software 3
1.3 Prerequisites 3
PART A: PROBABILITYAND RANDOM VARIABLES 5
2 BASIC PROBABILITY CONCEPT S 7
2.1 Elements of Set Theory 8
2.1.1 Set Operations 9
2.2 Sample Space andProbability Measure 12
2.2.1 Axioms ofProbability 13
2.2.2 Assignment ofProbability 16
2.3 Statistical Independence 17
2.4 Conditional Probability 20
Reference 28
Further Reading 28
Problems 28
3 RANDOM VARIABLES A ND PROBABILITY
DISTRIBUTIONS 37
3.1 Random Variables 37
3.2 Probability D istributions 39
3.2.1 Probability D istribution Function 39
3.2.2 Probability M ass F unction for D iscrete Random
Variables 41
TLFeBOOK
[...]... reliance on the use of probabilistic formulations in most scientific disciplines in the future Fundamentals ofProbability and StatisticsforEngineers T. TSoong ! 2004 John Wiley & Sons, Ltd ISBNs: 0-4 7 0-8 681 3-9 (HB) 0-4 7 0-8 681 4-7 (PB) TLFeBOOK 8 2.1 F undamentals ofProbabilityandStatisticsforEngineers ELEMENTS OF SET THEORY Our interest in the study of a random phenomenon is in the statements we can... large For example, the outcome of flipping a coin is not predictable but there is statistical regularity in that the ratio m/n approaches 1 for either 2 Fundamentals ofProbability and StatisticsforEngineers T. TSoong Ó 2004 John Wiley & Sons, Ltd ISBNs: 0-4 7 0-8 681 3-9 (HB) 0-4 7 0-8 681 4-7 (PB) TLFeBOOK 2 Fundamentals ofProbability and StatisticsforEngineers heads or tails Random phenomena in scientific... prepared to do this strongly depends on his or her mastery of the fundamentals It is important that the student develop an early appreciation for applications D emonstrations of the utility of this material in nonsuperficial applications not only sustain student interest but also provide the student with stimulation to delve more deeply into the fundamentals Most of the students in engineering and applied... probabilityand we need the additional information, P (AB) , which is the probabilityof having between 40 and 50 cars turning left With the statement of three axioms of probability, we have completed the mathematical description of a random experiment It consists of three fundamental constituents: a sample space S , a collection of events A, B, , and the probability function P These three quantities... leads to the recognition that a great deal of uncertainty and variability are inevitably present in problem formulation, and one of the mathematical tools that is effective in dealing with them is probabilityandstatistics Probabilistic ideas are used in a wide variety of scientific investigations involving randomness Randomness is an empirical phenomenon characterized by the property that the quantities... concerning the events that can occur Events and combinations of events thus play a central role in probability theory The mathematics of events is closely tied to the theory of sets, and we give in this section some of its basic concepts and algebraic operations A set is a collection of objects possessing some common properties These objects are called elements of the set and they can be of any kind with any... devote one semester or two quarters to a course of this nature in their programs R ecognizing that the coverage is time limited, it is important that the material be self-contained, representing a reasonably complete and applicable body of knowledge The choice of the contents for this book is in line with the foregoing observations The major objective is to give a careful presentation of the fundamentals. .. Distribution 7.4.2 Chi-Squared Distribution 7.5 Beta and R elated Distributions 7.5.1 Probability Tabulations 7.5.2 Generalized Beta Distribution 7.6 Extreme-Value Distributions 7.6.1 Type-I Asymptotic D istributions of Extreme Values 7.6.2 Type-II Asymptotic Distributions of Extreme Values 7.6.3 Type-III Asymptotic Distributions of Extreme Values 7.7 Summary R eferences F urther R eading and Comments Problems... relative frequency clearly possesses the properties required of the probability measure and is a natural candidate for the probabilityof A This interpretation is used, for example, in saying that the TLFeBOOK 17 Basic Probability Concepts probabilityof ‘heads’ in flipping a coin is 1/2 The relative frequency approach to probability assignment is objective and consistent with the axioms stated in Section... that are subsets of space S The union or sum of A and B, denoted by A B, is the set of all elements belonging to A or B or both S A Figure 2.2 A A and A TLFeBOOK 10 F undamentals ofProbabilityandStatisticsforEngineers B A B A (a) A ∪ B (b) A ∩ B Figure 2.3 (a) U nion and (b) intersection of sets A and B The intersection or product of A and B, written as A B, or simply AB, is the set of . TLFeBOOK FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS T. T. Soong State University of New York at Buffalo, Buffalo, New York, USA TLFeBOOK TLFeBOOK FUNDAMENTALS OF PROBABILITY AND STATISTICS. 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. important that the student develop an early appreciation for applica- tions. D emonstrations of the utility of this material in nonsuperficial applica- tions not only sustain student interest but