Mathematical Statistics With Applications Pdf

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1. 1. Mathematical Statistics with Applications
2. 2. To adopt this book for course use, visit http://textbooks.elsevier.com Companion Web Site: http://www.elsevierdirect.com/companions/9780123748485 ELSEVIERscience & technology books Resources for Professors: Links to Web sites carefully chosen to supplement the content of the textbook. Online Student Solutions Manual is now available through separate purchase. Mathematical Statistics with Applications, password Also available with purchase of protected and activated upon registration, online Instructors Solutions Manual. Mathematical Statistics with Applications by Kandethody M. Ramachandran and Chris P. Tsokos ACADEMIC PRESS TOOLS ALL TEACHINGFOR YOUR NEEDS textbooks.elsevier.com All figures from the book available as PowerPoint slides and as jpegs.
3. 3. Mathematical Statistics with Applications KandethodyM.Ramachandran DepartmentofMathematicsandStatistics UniversityofSouthFlorida Tampa,FL ChrisP.Tsokos DepartmentofMathematicsandStatistics UniversityofSouthFlorida Tampa,FL AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an imprint of Elsevier
4. 4. Elsevier Academic Press 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, California 92101-4495, USA 84 Theobalds Road, London WC1X 8RR, UK This book is printed on acid-free paper. Copyright 2009, 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 photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elseviers Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.co.uk. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting Customer Support and then Obtaining Permissions. Library of Congress Cataloging-in-Publication Data Ramachandran, K. M. Mathematical statistics with applications / Kandethody M. Ramachandran, Chris P. Tsokos. p. cm. ISBN 978-0-12-374848-5 (hardcover : alk. paper) 1. Mathematical statistics. 2. Mathematical statisticsData processing. I. Tsokos, Chris P. II. Title. QA276.R328 2009 519.5dc22 2008044556 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 13: 978-0-12-374848-5 For all information on all Elsevier Academic Press publications visit our Web site at www.elsevierdirect.com Printed in the United States of America 09 10 9 8 7 6 5 4 3 2 1
5. 5. Dedicated to our families: Usha, Vikas, Vilas, and Varsha Ramachandran and Debbie, Matthew, Jonathan, and Maria Tsokos
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7. 7. Contents Preface................................................................................................... xv Acknowledgments ...................................................................................... xix About the Authors....................................................................................... xxi Flow Chart ..............................................................................................xxiii CHAPTER 1 Descriptive Statistics............................................................. 1 1.1 Introduction ...................................................................... 2 1.1.1 Data Collection ......................................................... 3 1.2 Basic Concepts .................................................................. 3 1.2.1 Types of Data ........................................................... 5 1.3 Sampling Schemes .............................................................. 8 1.3.1 Errors in Sample Data.................................................. 11 1.3.2 Sample Size............................................................. 12 1.4 Graphical Representation of Data .............................................. 13 1.5 Numerical Description of Data ................................................. 26 1.5.1 Numerical Measures for Grouped Data ............................... 30 1.5.2 Box Plots ............................................................... 33 1.6 Computers and Statistics ........................................................ 39 1.7 Chapter Summary ............................................................... 40 1.8 Computer Examples ............................................................. 41 1.8.1 Minitab Examples ...................................................... 41 1.8.2 SPSS Examples ........................................................ 46 1.8.3 SAS Examples.......................................................... 47 Projects for Chapter 1 ................................................................ 51 CHAPTER 2 Basic Concepts from ProbabilityTheory .......................................... 53 2.1 Introduction ...................................................................... 54 2.2 Random Events and Probability ................................................ 55 2.3 Counting Techniques and Calculation of Probabilities ........................ 63 2.4 The Conditional Probability, Independence, and Bayes Rule ................ 71 2.5 Random Variables and Probability Distributions .............................. 83 2.6 Moments and Moment-Generating Functions ................................. 92 2.6.1 Skewness and Kurtosis................................................. 98 2.7 Chapter Summary ............................................................... 107 2.8 Computer Examples (Optional)................................................. 108 2.8.1 Minitab Computations ................................................. 109 2.8.2 SPSS Examples ........................................................ 110 2.8.3 SAS Examples.......................................................... 110 Projects for Chapter 2 ................................................................ 112 vii
8. 8. viii Contents CHAPTER 3 AdditionalTopics in Probability .................................................. 113 3.1 Introduction ...................................................................... 114 3.2 Special Distribution Functions.................................................. 114 3.2.1 The Binomial Probability Distribution ................................ 114 3.2.2 Poisson Probability Distribution....................................... 119 3.2.3 Uniform Probability Distribution...................................... 122 3.2.4 Normal Probability Distribution....................................... 125 3.2.5 Gamma Probability Distribution ...................................... 131 3.3 Joint Probability Distributions .................................................. 141 3.3.1 Covariance and Correlation............................................ 148 3.4 Functions of Random Variables................................................. 154 3.4.1 Method of Distribution Functions ..................................... 154 3.4.2 The pdf of Y = g(X), Where g Is Differentiable and Monotone Increasing or Decreasing............................................... 156 3.4.3 Probability Integral Transformation ................................... 157 3.4.4 Functions of Several Random Variables: Method of Distribution Functions ............................................................... 158 3.4.5 Transformation Method ................................................ 159 3.5 Limit Theorems.................................................................. 163 3.6 Chapter Summary ............................................................... 173 3.7 Computer Examples (Optional)................................................. 175 3.7.1 Minitab Examples ...................................................... 175 3.7.2 SPSS Examples ........................................................ 177 3.7.3 SAS Examples.......................................................... 178 Projects for Chapter 3 ................................................................ 180 CHAPTER 4 Sampling Distributions .......................................................... 183 4.1 Introduction ...................................................................... 184 4.1.1 Finite Population ....................................................... 187 4.2 Sampling Distributions Associated with Normal Populations................. 191 4.2.1 Chi-Square Distribution................................................ 192 4.2.2 Student t-Distribution .................................................. 198 4.2.3 F-Distribution .......................................................... 202 4.3 Order Statistics .................................................................. 207 4.4 Large Sample Approximations.................................................. 212 4.4.1 The Normal Approximation to the Binomial Distribution ........... 213 4.5 Chapter Summary ............................................................... 218 4.6 Computer Examples ............................................................. 219 4.6.1 Minitab Examples ...................................................... 219 4.6.2 SPSS Examples ........................................................ 219 4.6.3 SAS Examples.......................................................... 219 Projects for Chapter 4 ................................................................ 221
9. 9. Contents ix CHAPTER 5 Point Estimation ................................................................. 225 5.1 Introduction ...................................................................... 226 5.2 The Method of Moments .............................

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