Evans - Rosenthal Cap. 1-4

Evans - Rosenthal Cap. 1-4 - Senior Acquisitions Edit.or:...

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Unformatted text preview: Senior Acquisitions Edit.or: Pati-ick Farace Development Editor: Danielle Swearangin New Media/Supplements Brian Donnellan Marketing Manager: Jeffrey Rocker Project Vivian Weiss Text Designer: Blake Logan Cover Image: Joan Spavins, Doorways, acrylic and watercolor on paper, 2002 Illustrations Composition: Michael 3. Evans, S. Rosenthal Director of Production: Ellen Cash Printing Binding: R. Donnelley © 2004 by W. H. Freeman Company. All rights reserved Printed in the United States America Second printing Company 41 Madison Avenue York, NY 10010 Houndznills, Basingatoke RG21 6XS, England www.whfreeman.com Contents Preface 1 Probability Models 1.1 Probability: A Mejj Uncej, 1.1.1 3 1o We Need Theory? 1.2 Probility Mod 1.2.1 Veon Diagrams Subsets 1.3 Properties Probabilit, 1.4 Uniform Probabffity 5p 1.4.1 Combinatorij Principles 1.5 Condjtjonei Probabjjjty lndepeude 1.5.1 Conditional 1.5.2 Indepewjen Evants 1.6 Continuity ‘ 2.7 Further Proof 5 (Advan) 2 Random Variables Distrjbutj 2.1 2.2 Distributions Radom VariaJ 2.3 Discrete fliibutions 2.3.1 Import Djrjbj 00 g 2.4 Continuous 2.4.1 Impor Absolutejy 2.5 Cumulative Distributi 2.5.1 Propjes Distribution Ftmctions 2.5.2 Cdfs 2.5.3 CriEs Ahsoluiy 2.5.4 Mixture 2.5.5 Neither Nor 2.6 One-Djrnjonal Change Variable 2.6.1 The C 2.6.2 ( J j 77 2.7.1 Joint Functions Library Congress Control Number: 2003108117 ix I 4 7 10 13 14 19 20 23 28 30 33 37 40 50 52 61 62 64 66 69 72 ‘U iv 2.7.2 Marginal DistributiOflS 2.7.3 Joint ProbabkhtY 2.7.4 Density F°° 2.8 Cooditj0n1 and depce 2.8.1 conditioning on Discrete Random Variables 2.8.2 Continuous 2.8.3 Independence of 2.8.4 Order 2.9 MultidimeflSm0 Change Variable 2.9.1 The Case 2.9.2 ContinuouS (Advanced) 2.9.3 ConvolutiOn 2.10 Simulating Probabmty flistributiofl5 2.10.1 Distributions 2,10.2 2.11 Further Proofs (Add) 3 Expectation 123 3.1 C 3.2 AbsolutelY Cofltjt1uous 135 3.3 Variance, Covariaflce, Correlation 142 3,4 Generating mctj005 154 3.4.1 CharacteristiC Functions 161 3,5 Conditi0Th 166 3.5.1 156 3,5.2 AbsolUtelY 168 3.5.3 Double xpectatmofls 169 3.5.4 conditional Variance 171 3.6 InequalitieS 176 3.6.1 Jensen’s InequalitY (Advaeced) 179 3.7 General ExpectationS 182 3.8 (Adad) 185 4 SamplIng Limits 189 4.1 Sampling DistnibutiOo5 190 4.2 Convergence Probability 193 4.2.1 Weak Law Large Numbers 195 43 (onvergenc with ProbabilitY 1 198 4.3.1 Strong 200 4.4 onvergeflC in Oistdbutj00 202 4.4.1 Central Limit Theorem 204 4,4.2 Assessing Error 209 4.5 Monte Carlo ApprOm5ti01 213 4.6 Normal Distribution Theory 222 4.6.1 ChiScluared 223 4.6.2 t Distributi0fl 226 CONTENTS v 4.6.3 F 227 4.7 231 5 Statistical Inference 239 5.1 Why Do We Need Statistics? 5.2 Using a Model 244 5.3 Models 247 5.4 Data Collection 254 5.4.1 Finite Populations 5.4.2 Simple 256 5.4.3 Histograms 259 5.4.4 Survey 261 5.5 Some Basic Inferences 266 5.5.1 Descriptive Statistics 267 5.5.2 Plotting 271 5.5.3 Types 273 6 Likelihood 281 6.1 Function 6.1.1 Sufficient 286 6.2 Maximum Estimation 291...
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This note was uploaded on 11/24/2010 for the course DSE 101 taught by Professor Agostinelli during the Winter '10 term at Università Ca' Foscari.

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Evans - Rosenthal Cap. 1-4 - Senior Acquisitions Edit.or:...

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