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1、10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A2010－2011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
2、。题号123总分分值256015得分评卷人1．FILLINGTHEBLANKS(25points)(1)Inabagtherearemwhiteballs,nblackballsandsgreenballswithm+n+s>3.Ifwedrawoneballfromthebag,theprobabilityoftheballbeingawhiteoneis.Ifwedrawtheballonebyonefromthebagwithoutreplacement,theprobabilitythatthesec
3、ondballdrawniswhiteis.(2)SupposeD(X/2)=9,D(X-Y)=62,D(X+Y)=42.Thenthecorrelationcoefficient-5/24.(3)Ifarandomvariablehasmeanandstandarddeviation,Chebyshev’stheoremtellusthat_______.《》试卷第10页共10页10(4)Forthesetofnumbers{1,-1,2,-3,4,6},themeanis______,themediani
4、s_______,therangeis_______,themeandeviationis_______,thevarianceis_______,thestandarddeviationis________.(5)Supposeisthesamplevaranceofarandomsampleofsizemfromapopulationthatfollowsanormaldistribution.Then~2.COMPUTATIONS:(60points)(1).Thereare7ballsinabagwi
5、theachballbeingwhiteorblack,butwedon’tknowthenumberofblackballs(andofcoursethenumberofwhiteballsisalsounknown).Threeballsaredrawnatrandomfromthebagatonceandwefindoneisblackandtwoarewhite.Estimatethenumberoftheblackballsusingthemethodofmaximumlikelihood.Solu
6、tion:Assumethatthereareiblackballs,thepossibilityforthiseventstohappenis(2).Afactoryprducesmachines.Thecostofeachmachineproducedis$2000,andthesellingpriceis$4000.IfthenumberXofmathinessoldhasthedistributionasfollows:《》试卷第10页共10页10x0123456P(X=x)0.10.10.150.2
7、0.20.150.1Howmanymachinesthatthefactoryshouldproducedtomaximizetheexpectationofitsprofit?Solution:Weneedtofindthelargestisuchthatthisisgreaterthanzero.Andthenwefindthattomaximizetheexpectationofitsprofits,3machinesshouldbeproduced.(3).LetXbearandomvariableh
8、avingthebinmialdistributionwithparametersnandp,showthatisanumbiasedestimatorofthevarianceofX.《》试卷第10页共10页10(4).Ifarandomvariablehasanormaldistribution,whataretheprobabilitiesthatitwilltakeonavaluewithi
