QMS 102 Lecture 7: Lecture 7

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Prob. of getting a head on a coin toss. Prob. of an increase in taxes this year. Approachestoprobability: subjective, experimental(orrelativefrequency, theoretical(orclassical, allprobabilitiesarebetween0and1inclusive, theprobabilityofaneventwhichcannotoccuris0, theprobabilityofaneventwhichoccurwith certaintyis1, theprobabilityofaneventnotoccurringisone minustheprobabilityofitoccurring. Ifalltheoutcomesinthesamplespaceareequallylikely,then in the the sample the sample outcomes in in number number number of of of outcomes outcomes event. Example: space space p green marble of of. Number red red of marbles marbles marbles in in in the the the bag bag bag. X[5,7]min discrete random variable may assume either a finite number. A discrete random variable of values or an infinite sequence of values. Count cars at toll betw een 11:00 & 1:00. X p x j j: calculateameanforadiscreteprobabilitydistributionisthesameascalculating aweightedmean. Acompanyisinprocessoftryingtodecidewhetherornotto marketaparticularnewproductthatitisconsidering. a marketanalysishasdeterminedthattheprobabilitiesof variousacceptancelevelsareasfollows:highwitha probabilityof0. 2,mediumwithaprobabilityof0. 5,andlow withaprobabilityof0. 3. ifthecompanydecidestobuilda localmanufacturingfacility,theestimatedprofitsoverthelife of the product if there is high acceptance is million if oftheproductifthereishighacceptanceismillion,if thereismediumacceptancetheprofitshouldbearound millionandifthereislowacceptancetherewillbealossof million. . Acompanyisinprocessoftryingtodecidewhetherornottomarketa particularnewproductthatitisconsidering. amarketanalysishas determinedthattheprobabilitiesofvariousacceptancelevelsareas follows:highwithaprobabilityof0. 2,mediumwithaprobabilityof0. 5, andlowwithaprobabilityof0. 3. ifthecompanydecidestobuildalocal manufacturingfacility,theestimatedprofitsoverthelifeoftheproductif thereishighacceptanceismillion,ifthereismediumacceptancethe profitshouldbearoundmillionandifthereislowacceptancetherewill bealossofmillion. . Afastfoodcompanyplanstoinstallanewicehcreamdispensingunitinoneoftwo storelocations. thecompanyfiguresthattheprobabilityofaunitbeing successfulinlocationais andtheannualprofitinthiscaseis,000. ifitis notsuccessfultherewillbelossesof,000. atlocationbtheprobabilityof succeedingis butthepotentialprofitandlossare,000and,000 respectively. a) b)

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