a natural introduction to probability theory

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1、RonaldMeesterANaturalIntroductiontoProbabilityTheorySecondEditionBirkhäuserBaselëBostonëBerlinAuthor:RonaldMeesterFaculteitderExacteWetenschappenVrijeUniversiteitDeBoelelaan1081a1081HVAmsterdamTheNetherlandse-mail:rmeester@cs.vu.nl2000MathematicsSubjectClassification60-01Lib

2、raryofCongressControlNumber:2007942638BibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetat.ISBN978-3-7643-8723-5BirkhäuserVerl

3、ag,Basel–Boston–BerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Forany

4、kindofusepermissionofthecopyrightownermustbeobtained.Firstedition2003©2008BirkhäuserVerlagAGBasel·Boston·BerlinP.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaPrintedonacid-freepaperproducedfromchlorine-freepulp.TCFÇPrintedinGermanyISBN978-3-7643-8723-

5、5e-ISBN978-3-7643-8724-2987654321www.birkhauser.chContentsPrefacetotheFirstEditionviiiPrefacetotheSecondEditionx1Experiments11.1DefinitionsandExamples.......................11.2CountingandCombinatorics.....................61.3PropertiesofProbabilityMeasures..................

6、101.4ConditionalProbabilities........................121.5Independence..............................181.6AFirstLawofLargeNumbers....................261.7Exercises................................282RandomVariablesandRandomVectors352.1RandomVariables..........................

7、.352.2Independence..............................412.3ExpectationandVariance.......................432.4RandomVectors............................522.5ConditionalDistributionsandExpectations.............572.6GeneratingFunctions..........................622.7Exercises.........

8、.......................643RandomWalk713.1RandomWalkandCounting....................