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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
2、总分分值256015得分评卷人1．FILLINGTHEBLANKS(25points)(1)Inabagtherearemwhiteballs,nblackballsandsgreenballswithm+n+s>3.Ifwedrawoneballfromthebag,theprobabilityoftheballbeingawhiteoneis ________________.Ifwedrawtheballonebyonefromthebagwithoutreplacement,theprobabilitythat
3、thesecondballdrawniswhiteis__________________.(2)SupposeD(X/2)=9,D(X-Y)=62,D(X+Y)=42.Thenthecorrelationcoefficient______________.(3)Ifarandomvariablehasmeanandstandarddeviation,Chebyshev’stheoremtellusthat_____________.《概率统计》试卷第8页共8页8(4)Forthesetofnumbers{1,-1,2,
4、-3},themeanis______,themedianis_______,therangeis_______,themeandeviationis_______,thevarianceis_______,thestandarddeviationis________.(5)Supposeisthesamplevaranceofarandomsampleofsizemfromapopulationthatfollowsanormaldistribution.Thenthevariable_____________~(6)
5、AssumethatbinomialdistributionsX~B(m,p)andY~B(n,p)areindependent,thenX+Y~_______.(7)Throwacoinuntillaheadshows,theexpectationofthenumberoftossingis___________.2.COMPUTATIONS:(60points)(1).Thereare7ballsinabagwitheachballbeingwhiteorblack,butwedon’tknowthenumberof
6、blackballs(andofcoursethenumberofwhiteballsisalsounknown).Threeballsaredrawnatrandomfromthebagatonceandwefindoneisblackandtwoarewhite.Estimatethenumberoftheblackballsusingthemethodofmaximumlikelihood.(2).Afactoryprducesmachines.Thecostofeachmachineproducedis$2000
7、,andthesellingpriceis$4000.IfthenumberXofmathinessoldhasthedistributionasfollows:《概率统计》试卷第8页共8页8x0123456P(X=x)0.10.10.150.20.20.150.1Howmanymachinesthatthefactoryshouldproducetomaximizetheexpectationofitsprofit?(Hint:If1machineisproduced,whatistheexpectationofpro
8、fit?)(3).LetXbearandomvariablehavingthebinmialdistributionwithparametersnandp,showthatisanumbiasedestimatorofthevarianceofX.(4).Ifarandomvariablehasanormaldist
