...A Solution Manual for: A First Course In Probability: Seventh Edition by Sheldon M. Ross. John L. Weatherwax∗ September 4, 2007 Introduction Acknowledgements Special thanks to Vincent Frost and Andrew Jones for helping find and correct various typos in these solutions. Miscellaneous Problems The Crazy Passenger Problem The following is known as the “crazy passenger problem” and is stated as follows. A line of 100 airline passengers is waiting to board the plane. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let’s say that the k-th passenger in line has a ticket for the seat number k.) Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random. What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)? If one tries to solve this problem with conditional probability it becomes very difficult. We begin by considering the following cases if the first passenger sits in seat number 1, then all ∗ wax@alum.mit.edu 1 the remaining passengers will be in their correct seats and certainly the #100’th will also. If he sits in the last seat #100, then certainly the last passenger cannot sit there (in fact he will end up in seat #1). If he sits in any of the 98...
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...Op"erations Research This page intentionally left blank Copyright © 2007, 2005 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2944-2 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com PREFACE I started my teaching career in the year 1964. I was teaching Production Engineering subjects till 1972. In the year 1972 I have registered my name for the Industrial Engineering examination at National Institution of Industrial Engineering, Bombay. Since then, I have shifted my field for interest to Industrial Engineering subjects and started teaching related subjects. One such subject is OPERATIONS RESEARCH. After teaching these subjects till my retirement in the year 2002, it is my responsibility to help the students with a book on Operations research. The first volume of the book is LINEAR PORGRAMMING MODELS. This was published in the year 2003. Now I am giving this book OPERATIONS RESEARCH, with other chapters to students, with a hope that it will help them to understand...
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...Vijay V. Vazirani College of Computing Georgia Institute of Technology Copyright c 2001 Approximation Algorithms Springer Berlin Heidelberg NewYork Barcelona Hong Kong London Milan Paris Singapore Tokyo To my parents Preface Although this may seem a paradox, all exact science is dominated by the idea of approximation. Bertrand Russell (1872–1970) Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed conjecture that P = NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of approximation algorithms as it stands today. It is reasonable to expect the picture to change with time. The book is divided into three parts. In Part I we cover a combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. The latter may give Part I a non-cohesive appearance. However, this is to be expected – nature is very rich, and we cannot expect a few tricks to help solve the diverse collection of NP-hard problems. Indeed, in this part, we have purposely refrained from tightly categorizing algorithmic techniques so as not to trivialize matters. Instead, we have attempted to capture, as accurately as possible, the individual character...
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...Fundamentals of Database Systems Preface....................................................................................................................................................12 Contents of This Edition.....................................................................................................................13 Guidelines for Using This Book.........................................................................................................14 Acknowledgments ..............................................................................................................................15 Contents of This Edition.........................................................................................................................17 Guidelines for Using This Book.............................................................................................................19 Acknowledgments ..................................................................................................................................21 About the Authors ..................................................................................................................................22 Part 1: Basic Concepts............................................................................................................................23 Chapter 1: Databases and Database Users..........................................................................................23 ...
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...Chaotic Growth with the Logistic Model of P.-F. Verhulst Hugo Pastijn Department of Mathematics, Royal Military Academy B-1000 Brussels, Belgium Hugo.Pastijn@rma.ac.be Summary. Pierre-Fran¸ois Verhulst was born 200 years ago. After a short biograc phy of P.-F. Verhulst in which the link with the Royal Military Academy in Brussels is emphasized, the early history of the so-called “Logistic Model” is described. The relationship with older growth models is discussed, and the motivation of Verhulst to introduce different kinds of limited growth models is presented. The (re-)discovery of the chaotic behaviour of the discrete version of this logistic model in the late previous century is reminded. We conclude by referring to some generalizations of the logistic model, which were used to describe growth and diffusion processes in the context of technological innovation, and for which the author studied the chaotic behaviour by means of a series of computer experiments, performed in the eighties of last century by means of the then emerging “micro-computer” technology. 1 P.-F. Verhulst and the Royal Military Academy in Brussels In the year 1844, at the age of 40, when Pierre-Fran¸ois Verhulst on November c 30 presented his contribution to the “M´moires de l’Acad´mie” of the young e e Belgian nation, a paper which was published the next year in “tome XVIII” with the title: “Recherches math´matiques sur la loi d’accroissement de la e population” (mathematical investigations of the law of...
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...THIRD EDITI ----- --·-- --·-- - - -- - O N -- SU PP LY CH AI N MA NA GE ME NT Stra tegy , Plan ning , and Ope ratio n Sunil Chopra Kellogg Schoo l of Manag ement Northwestern University Peter Meindl Stanfo rd University --------Prentice I-I all Uppe r Saddl e River , New Jersey ·--· PEAR SON -- · - · - - - "ibrary of Congress Cataloging-in-Publication Data :::hopra, Sunil Supply chain management: strategy, planning, and operation I Sunil Chopra, >eter Meind!.-3rd ed. p. em. Includes bibliographical references and index. ISBN: 0-13-208608-5 1. Marketing channels-Managemen t. 2. Delivery of goods-Management. i. Physical distribution of goods-Management. 4. Customer servicesvfanagement. 5. Industrial procurement. 6. Materials management. I. vfeindl, Peter II. Title. HF5415.13.C533 2007 658.7-dc22 2006004948 \VP/Executive Editor: Mark Pfaltzgraff ii:ditorial Director: Jeff Shelstad ;enior Project Manager: Alana Bradley E:ditorial Assistant: Barbara Witmer Vledia Product Development Manager: Nancy Welcher \VP/Executive Marketing Manager: Debbie Clare Vlarketing Assistant: Joanna Sabella ;enior Managing Editor (Production): Cynthia Regan flroduction Editor: Melissa Feimer flermissions Supervisor: Charles Morris Vlanufacturing Buyer: Michelle Klein Vlanager, Print Production: Christy Mahon Composition/Full-Service Project Management: Karen Ettinger, TechBooks, Inc. flrinter/Binder: Hamilton Printing Company Inc. fypeface: 10/12 Times Ten Roman :::redits...
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...THIRD EDITI ----- --·-- --·-- - - -- - O N -- SU PP LY CH AI N MA NA GE ME NT Stra tegy , Plan ning , and Ope ratio n Sunil Chopra Kellogg Schoo l of Manag ement Northwestern University Peter Meindl Stanfo rd University PEAR SON --------Prentice I-I all Uppe r Saddl e River , New Jersey ·--· -- · - · - - - "ibrary of Congress Cataloging-in-Publication Data :::hopra, Sunil Supply chain management: strategy, planning, and operation I Sunil Chopra, >eter Meind!.-3rd ed. p. em. Includes bibliographical references and index. ISBN: 0-13-208608-5 1. Marketing channels-Managemen t. 2. Delivery of goods-Management. i. Physical distribution of goods-Management. 4. Customer servicesvfanagement. 5. Industrial procurement. 6. Materials management. I. vfeindl, Peter II. Title. HF5415.13.C533 2007 658.7-dc22 2006004948 \VP/Executive Editor: Mark Pfaltzgraff ii:ditorial Director: Jeff Shelstad ;enior Project Manager: Alana Bradley E:ditorial Assistant: Barbara Witmer Vledia Product Development Manager: Nancy Welcher \VP/Executive Marketing Manager: Debbie Clare Vlarketing Assistant: Joanna Sabella ;enior Managing Editor (Production): Cynthia Regan flroduction Editor: Melissa Feimer flermissions Supervisor: Charles Morris Vlanufacturing Buyer: Michelle Klein Vlanager, Print Production: Christy Mahon Composition/Full-Service Project Management: Karen Ettinger, TechBooks, Inc. flrinter/Binder: Hamilton Printing Company Inc. fypeface:...
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...GNU Scientific Library Reference Manual Edition 1.14, for GSL Version 1.14 4 March 2010 Mark Galassi Los Alamos National Laboratory Jim Davies Department of Computer Science, Georgia Institute of Technology James Theiler Astrophysics and Radiation Measurements Group, Los Alamos National Laboratory Brian Gough Network Theory Limited Gerard Jungman Theoretical Astrophysics Group, Los Alamos National Laboratory Patrick Alken Department of Physics, University of Colorado at Boulder Michael Booth Department of Physics and Astronomy, The Johns Hopkins University Fabrice Rossi University of Paris-Dauphine Copyright c 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 The GSL Team. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with the Invariant Sections being “GNU General Public License” and “Free Software Needs Free Documentation”, the Front-Cover text being “A GNU Manual”, and with the Back-Cover Text being (a) (see below). A copy of the license is included in the section entitled “GNU Free Documentation License”. (a) The Back-Cover Text is: “You have the freedom to copy and modify this GNU Manual.” Printed copies of this manual can be purchased from Network Theory Ltd at http://www.network-theory.co.uk/gsl/manual/. The money raised from sales of the manual...
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