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1、8姓名学号学院专业座位号(密封线内不答题)……………………………………………………密………………………………………………封………………………………………线……………………………………线………………………………………_____________________…诚信应考,考试作弊将带来严重后果！华南理工大学期末考试《概率统计（双语）》试卷B2010－2011学年度下学期注意事项：1.考前请将密封线内各项信息填写清楚；2.填空题答在试卷上，其余题答在答题卷上。3．考试形式：闭卷；满分：100分4．考试时间120分钟。题号123总分分值206515得分评卷人1．FILLINGTHEBLAN
2、KS(20points)(1)Inabagtherearemwhiteballs,nblackballsandsgreenballswithm+n+s>3.(a)Ifwedrawoneballfromthebag,theprobabilityoftheballbeingblackoneis______________.(b)Ifwedrawtheballonebyonefromthebagwithoutreplacement,theprobabilitythatthesecondballdrawnisblackis___________________.(2)Iftheprobab
3、ilitydensityofarandomvariableXisgivenby,weknowthat_______,theprobabilityforXtotakeavaluebetween0.5and1.5is__________.《概率统计》试卷第8页共8页8(3)Suppose,XandYareindependent.Then2X+Y~____________.(4)Assumethatareindependent,Xfollowsuniformdistributionon[1,3],Yfollowsesponentialdistributionwithexpectation
4、,thejointdensityfunctionofis_____________________.(5)Letbeavariablefollowinganexponentialdistributionwithvariance,thedensityfunctionofis________________.(6).LetXbearandomvariablehavingthebinmialdistributionwithparametersnandp,ifisanumbiasedestimatorofthevarianceofX,thevalueofkis___________.2.C
5、OMPUTATIONS:(65points)(1).Afamilyhastwochildren.Ifweknowoneofthemisaboy,what’stheprobabilitythattheotherisagirl.(2).AssumethatyouaregoingtohaveinterviewsfromthreecompaniesA,BandC.Assumethataftereachinterview,youwillbeofferedoneofthefoursalaries0k,5k,6k,8k,withpossibility0.1,0.4,0.3,0.2respecti
6、velyrightaftertheinterviewandyouneedtodecidetoaccepttheofferornot,andyoushouldnottakethenextinterviewonceyouaccept.Makeaninterviewstrategytomaximizetheexpectationofthesalary.《概率统计》试卷第8页共8页8(Notethat0kmeansactuallynoofferbecauseyouwillnottakeajobwithoutsalary.Andifyouareoffered0kinthefirstcompa
7、nyA,obviouslyyouwillnottakeitandgotothenextinterview.Butityougeta8kofferyouwillcertaintakeitandnotgoforthenextinterview,thusforcompanyA,thequestionistoaskwhetheryouwilltakea5kofferandwheteryouwilltakea6koffer.)(3).Weknowthattheheightofp
