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1、13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A2009－2010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.所有答案请答在试卷，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256015
2、得分评卷人1．FILLINGTHEBLANKS(25points)(1)Inabagtheremwhiteballsandnblackballswithm+n>2.Ifwedrawoneballfromthebag,theprobabilityoftheballbeingawhiteoneis.Ifwedrawtwoballsfromthebag,theprobabilitythattwoballsareallwhiteis.Ifwedrawtheballonebyonefromthebagwithoutreplacement,the
3、probabilitythatthesecondballdrawniswhiteis.(2)IftheprobabilitydensityofarandomvariableXisgivenby,1/3,theprobabilityforXtotakeavaluebetween0.5and1.5is7/8.《》试卷第13页共13页13(3)SupposeD(X)=36,D(X-Y)=62,D(X+Y)=42.Thenthecorrelationcoefficient-5/24.(4)Ifarandomvariablehasmeanand
4、standarddeviation,Chebyshev’stheoremtellusthat.(5)SupposeY=2X+1,,Thus.(6)Letbeadistributionwithdegree,then.(7)Letbeavariablefollowinganexponentialdistributionwithmean,thedensityfunctionofis.(8)Let,andareindependent,isan-distributionwithdegreeand,i.e..2.COMPUTATIONS:(60p
5、oints)《》试卷第13页共13页13(1).Thereare4whiteballsand6blackballsinabag.Aballisdrawnatrandomfromthebagandaballofanothercoloristhenputintothebag.Thenasecondballisdrawn.Ifthetwoballsdrawnareofthesamecolor,whatistheprobabilitythattheyarebothblack?Solution:setandastheeventsofthetwo
6、ballsareallblack,white,andofthesamecolor,respectively.Then,Thustheprobabilityis.(2).Asupermarketisdoinganadcompaignbyorganizingaluckyraffledrawforevery100purchasers.Therulesisthateveryonewritehisownnameonacard,putthecardintoalotterybox,thusthereare100namesinthebox.Nowev
7、eryonedrawacardfromtheboxwithoutreplacement,onebyone.Theonewhodrawthecardwithhisownnamegeta50%discountonthepurchasing.Whatistheprobabilitythatnoonewillgetthediscount?(Assumethatthe100purchasershavedifferentnames.)Solution:Numberthepurchaserfrom1to100.Denoteastheeventsof
8、numbergetadiscount.Then《》试卷第13页共13页13Theprobabilitythatnoonewillgetthediscountis(3).Adieissoweightedthatforany
