analytic-aids

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1、Analytic Aids Probability Examples c7 Leif Mejlbro Download free books at LeifMejlbroProbabilityExamplesc-7AnalyticAids2ProbabilityExamplesc-7–AnalyticAids©2009LeifMejlbro&VentusPublishingApSISBN978-87-7681-523-33AnalyticAidsContentsContentsIntroduction51G

2、eneratingfunctions;background61.1Denitionofthegeneratingfunctionofadiscreterandomvariable61.2Somegeneratingfunctionsofrandomvariables71.3Computationofmoments81.4Distributionofsumsofmutuallyindependentrandomvariables81.5Computationofprobabilities91.6Converg

3、enceindistribution92TheLaplacetransformation;background102.1DenitionoftheLaplacetransformation102.2SomeLaplacetransformsofrandomvariables112.3Computationofmoments122.4Distributionofsumsofmutuallyindependentrandomvariables122.5Convergenceindistribution133Ch

4、aracteristicfunctions;background143.1Denitionofcharacteristicfunctions143.2Characteristicfunctionsforsomerandomvariables163.3Computationofmoments173.4Distributionofsumsofmutuallyindependentrandomvariables183.5Convergenceindistribution194Generatingfunctions

5、205TheLaplacetransformation486Thecharacteristicfunction85Index1104AnalyticAidsIntroductionIntroductionThisistheeightbookofexamplesfromtheTheoryofProbability.Ingeneral,thistopicisnotmyfavourite,butthankstomyformercolleague,OleJørsboe,Isomehowmanagedtogetani

6、deaofwhatitisallabout.Weshall,however,inthisvolumedealwithsometopicswhichareclosertomyownmathematicalfields.Theprerequisitesforthetopicscane.g.befoundintheVentus:Calculus2seriesandtheVentus:ComplexFunctionTheoryseries,andallthepreviousVentus:Probabilityc1-c

7、6.Unfortunatelyerrorscannotbeavoidedinafirsteditionofaworkofthistype.However,theauthorhastriedtoputthemonaminimum,hopingthatthereaderwillmeetwithsympathytheerrorswhichdooccurinthetext.LeifMejlbro27thOctober20095AnalyticAids1.Generatingfunctions;background1G

8、eneratingfunctions;background1.1DefinitionofthegeneratingfunctionofadiscreterandomvariableThegeneratingfunctionsareusedasanalyticaidsofrandomvariableswhichonlyhavevaluesinN0,e.g.binomialdistributedorPoissondis