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Instructor’s Solutions ManualProbability andStatistical InferenceEighth EditionRobert V. HoggUniversity of IowaElliot A. TanisHope CollegeThe author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expresses or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.Reproduced by Pearson Prentice Hall from electronic files supplied by the author.Copyright ©2010 Pearson Education, Inc. Publishing as Pearson Prentice Hall, Upper Saddle River, NJ 07458.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, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.ISBN-13: 978-0-321-58476-2ISBN-10: 0-321-58476-7ContentsPreface v1 Probability 11.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Properties of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Methods of Enumeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Independent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Bayes’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Discrete Distributions 112.1 Random Variables of the Discrete Type . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Mathematical Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 The Mean, Variance, and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . 162.4 Bernoulli Trials and the Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . 192.5 The Moment-Generating Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6 The Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Continuous Distributions 273.1 Continuous-Type Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Exploratory Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 Random Variables of the Continuous Type . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 The Uniform and Exponential Distributions . . . . . . . . . . . . . . . . . . . . . . . . 453.5 The Gamma and Chi-Square Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 483.6 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.7 Additional Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 Bivariate Distributions 574.1 Distributions of Two Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 The Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3 Conditional Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 The Bivariate Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Distributions of Functions of Random Variables 695.1 Functions of One Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2 Transformations of Two Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 735.3 Several Independent Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4 The Moment-Generating Function Technique . . . . . . . . . . . . . . . . . . . . . . . 795.5 Random Functions Associated with Normal Distributions . . . . . . . . . . . . . . . . 815.6 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . …
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