Instructor’s Manual for
Introduction to Probability
and Statistics for
Engineers and Scientists
Sixth Edition
Sheldon M. Ross
University of Southern California
Los Angeles, CA, United States
,Academic Press is an imprint of Elsevier
125 London Wall, London EC2Y 5AS, United Kingdom
525 B Street, Suite 1650, San Diego, CA 92101, United States
50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States
The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom
Copyright © 2021 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 photocopying, recording, or any information storage and retrieval system,
without permission in writing from the publisher. Details on how to seek permission, further
information about the Publisher’s permissions policies and our arrangements with organizations such
as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website:
www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright by the
Publisher (other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience
broaden our understanding, changes in research methods, professional practices, or medical treatment
may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating
and using any information, methods, compounds, or experiments described herein. In using such
information or methods they should be mindful of their own safety and the safety of others, including
parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume
any liability for any injury and/or damage to persons or property as a matter of products liability,
negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas
contained in the material herein.
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
ISBN: 978-0-12-824346-6
For information on all Academic Press publications
visit our website at https://www.elsevier.com/books-and-journals
Publisher: Katey Birtcher
Editorial Project Manager: Sara Valentino
Production Project Manager: Rukmani Krishnan
Designer: Patrick Ferguson
Typeset by VTeX
,Contents
Chapter 1 .............................................................................. 1
Chapter 2 .............................................................................. 2
Chapter 3 .............................................................................. 5
Chapter 4 ............................................................................ 11
Chapter 5 ............................................................................ 18
Chapter 6 ............................................................................ 23
Chapter 7 ............................................................................ 26
Chapter 8 ............................................................................ 31
Chapter 9 ............................................................................ 36
Chapter 10 .......................................................................... 39
Chapter 11 .......................................................................... 41
Chapter 12 .......................................................................... 42
Chapter 13 .......................................................................... 43
Chapter 14 .......................................................................... 45
Chapter 15 .......................................................................... 48
iii
, Chapter 1
1. Method (c) is probably best, with (e) being the second best.
2. In 1936 only upper middle class and rich people had telephones. Almost
all voters have telephones today.
3. No, these people must have been prominent to have their obituaries in
the New York Times; as a result they were probably less likely to have died
young than a randomly chosen person.
4. Locations (i) and (ii) are clearly inappropriate; location (iii) is probably
best.
5. No, unless it believed that whether a person returned the survey was in-
dependent of that person’s salary; probably a dubious assumption.
6. No, not without additional information as to the percentages of pedes-
trians that wear light and that wear dark clothing at night.
7. He is assuming that the death rates observed in the parishes mirror that
of the entire country.
8. 12,246/.02 = 612,300
9. Use them to estimate, for each present age x, the quantity A(x), equal to
the average additional lifetime of an individual presently aged x. Use this
to calculate the average amount that will be paid out in annuities to such
a person and then charge that person 1 + a times that latter amount as
a premium for the annuity. This will yield an average profit rate of a per
annuity.
10. 64 percent, 10 percent, and 48 percent.
1
Introduction to Probability
and Statistics for
Engineers and Scientists
Sixth Edition
Sheldon M. Ross
University of Southern California
Los Angeles, CA, United States
,Academic Press is an imprint of Elsevier
125 London Wall, London EC2Y 5AS, United Kingdom
525 B Street, Suite 1650, San Diego, CA 92101, United States
50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States
The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom
Copyright © 2021 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 photocopying, recording, or any information storage and retrieval system,
without permission in writing from the publisher. Details on how to seek permission, further
information about the Publisher’s permissions policies and our arrangements with organizations such
as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website:
www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright by the
Publisher (other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience
broaden our understanding, changes in research methods, professional practices, or medical treatment
may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating
and using any information, methods, compounds, or experiments described herein. In using such
information or methods they should be mindful of their own safety and the safety of others, including
parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume
any liability for any injury and/or damage to persons or property as a matter of products liability,
negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas
contained in the material herein.
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
ISBN: 978-0-12-824346-6
For information on all Academic Press publications
visit our website at https://www.elsevier.com/books-and-journals
Publisher: Katey Birtcher
Editorial Project Manager: Sara Valentino
Production Project Manager: Rukmani Krishnan
Designer: Patrick Ferguson
Typeset by VTeX
,Contents
Chapter 1 .............................................................................. 1
Chapter 2 .............................................................................. 2
Chapter 3 .............................................................................. 5
Chapter 4 ............................................................................ 11
Chapter 5 ............................................................................ 18
Chapter 6 ............................................................................ 23
Chapter 7 ............................................................................ 26
Chapter 8 ............................................................................ 31
Chapter 9 ............................................................................ 36
Chapter 10 .......................................................................... 39
Chapter 11 .......................................................................... 41
Chapter 12 .......................................................................... 42
Chapter 13 .......................................................................... 43
Chapter 14 .......................................................................... 45
Chapter 15 .......................................................................... 48
iii
, Chapter 1
1. Method (c) is probably best, with (e) being the second best.
2. In 1936 only upper middle class and rich people had telephones. Almost
all voters have telephones today.
3. No, these people must have been prominent to have their obituaries in
the New York Times; as a result they were probably less likely to have died
young than a randomly chosen person.
4. Locations (i) and (ii) are clearly inappropriate; location (iii) is probably
best.
5. No, unless it believed that whether a person returned the survey was in-
dependent of that person’s salary; probably a dubious assumption.
6. No, not without additional information as to the percentages of pedes-
trians that wear light and that wear dark clothing at night.
7. He is assuming that the death rates observed in the parishes mirror that
of the entire country.
8. 12,246/.02 = 612,300
9. Use them to estimate, for each present age x, the quantity A(x), equal to
the average additional lifetime of an individual presently aged x. Use this
to calculate the average amount that will be paid out in annuities to such
a person and then charge that person 1 + a times that latter amount as
a premium for the annuity. This will yield an average profit rate of a per
annuity.
10. 64 percent, 10 percent, and 48 percent.
1
