資源描述：
《intro to mathematical statistics hogg chapter 1》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在工程資料-天天文庫。
1、Chapter1ProbabilityandDistributions1.1IntroductionManykindsofinvestigationsmaybecharacterizedinpartbythefactthatrepeatedexperimentation,underessentiallythesameconditions,ismoreorlessstandardprocedure.Forinstance,inmedicalresearch,interestmaycenteronthee?ectofadrugthatistobeadministered;oraneconomis
2、tmaybeconcernedwiththepricesofthreespeci?edcommoditiesatvarioustimeintervals;ortheagronomistmaywishtostudythee?ectthatachemicalfertilizerhasontheyieldofacerealgrain.Theonlywayinwhichaninvestigatorcanelicitinformationaboutanysuchphenomenonistoperformtheexperiment.Eachexperimentterminateswithanoutcom
3、e.Butitischaracteristicoftheseexperimentsthattheoutcomecannotbepredictedwithcertaintypriortotheperformanceoftheexperiment.Supposethatwehavesuchanexperiment,buttheexperimentisofsuchanaturethatacollectionofeverypossibleoutcomecanbedescribedpriortoitsperformance.Ifthiskindofexperimentcanberepeatedunde
4、rthesameconditions,itiscalledarandomexperiment,andthecollectionofeverypossibleoutcomeiscalledtheexperimentalspaceorthesamplespace.Example1.1.1.Inthetossofacoin,lettheoutcometailsbedenotedbyTandlettheoutcomeheadsbedenotedbyH.Ifweassumethatthecoinmayberepeatedlytossedunderthesameconditions,thenthetos
5、softhiscoinisanexampleofarandomexperimentinwhichtheoutcomeisoneofthetwosymbolsTandH;thatis,thesamplespaceisthecollectionofthesetwosymbols.Example1.1.2.Inthecastofonereddieandonewhitedie,lettheoutcomebetheorderedpair(numberofspotsuponthereddie,numberofspotsuponthewhitedie).Ifweassumethatthesetwodice
6、mayberepeatedlycastunderthesameconditions,thenthecastofthispairofdiceisarandomexperiment.Thesamplespaceconsistsofthe36orderedpairs:(1,1),...,(1,6),(2,1),...,(2,6),...,(6,6).LetCdenoteasamplespace,letcdenoteanelementofC,andletCrepresentacollectionofelementsofC.If,upontheperformanceoftheexperiment,th
7、eoutcome12ProbabilityandDistributionsisinC,weshallsaythattheeventChasoccurred.NowconceiveofourhavingmadeNrepeatedperformancesoftherandomexperiment.Thenwecancountthenumberfoftimes(thefrequency)thattheeventCa
