041 sc概率系统分析应用秋季成绩单讲座.pdfVIP

6.041SCProbabilisticSystemsAnalysisandAppliedProbability,Fall2013

Transcript–Lecture14

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PROFESSOR:Solasttimewestartedtalkingaboutrandomprocesses.Arandomprocessisa

randomexperimentthatevolvesovertime.Andconceptually,itsimportanttorealizethatitsa

singleprobabilisticexperimentthathasmanystages.Actually,ithasaninfinitenumberof

stages.Andwediscussedthesimplestrandomprocessthereis,theBernoulliprocess,whichis

nothingbutthesequenceofBernoullitrials--aninfinitesequenceofBernoullitrials.For

example,flippingacoinoverandover.

Onceweunderstandwhatsgoingonwiththatprocess,thenwhatwewantistomoveintoa

continuoustimeversionoftheBernoulliprocess.AndthisiswhatwewillcallthePoisson

process.AndforthePoissonprocess,weregoingtodoexactlythesamethingsthatwedidfor

theBernoulliprocess.Thatis,talkaboutthenumberofarrivalsduringagiventimeperiod,and

talkalsoaboutthetimweenconsecutivearrivals,andforthedistributionofinter-arrival

times.

Soletsstartwithaquickreviewofwhatwediscussedlasttime.First,anoteaboutlanguage.If

youthinkofcointosses,wethentalkaboutheadsandtails.Ifyouthinkoftheseasasequenceof

trials,youcantalkaboutsuccessesandfailures.Thelanguagethatwewillbeusingwillbemore

thelanguageofarrivals.Thatis,ifinagivenslotyouhaveasuccess,yousaythatsomething

arrived.Ifyouhaveafailure,nothingarrived.Andthatlanguageisalittlemoreconvenientand

morenatural,especiallywhenwetalkaboutcontinuoustime--totalkaboutarrivalsin