概率論與數(shù)理統(tǒng)計(jì)試題(英文)09.1.8

1、20082009第一學(xué)期«概率論與數(shù)理統(tǒng)計(jì)（ProbabilityandStatistics）»考試試卷（A卷）（閉卷）NameStudentIDClassScoreSignatureDate:Jan8,2009Time:8:30amto11:00amInstruction:Answerallquestionsinthespaceprovided.Showyourwork.Question12345678totalMarkQuestion1(21points)Fillingtheblanks(1) .LetA,Bbetwoevents,P(A)=0.4,P(B)=0.3,P

2、(AUb)=0.6,thenP(ab)(2) .SupposearandomvariableXhastheprobabilitydistributionwith(3).2-201©30.10.220.4,thenP(X2-1)=Suppose(X,Y)hasthejointdensityfunction2,x>0,y>0,x+y<1f(x,y)=,thenthemarginaldistributionforXalone0,elsewhereg(x)=2(4) .SupposeXN(，；-),consideraquadraticequationwithoneunkno

3、wn2y2yX=0abouty,iftheprobabilityofthisequationhavingnorealrootis1,thenJ-二(5) .Thenumberofdistinctpermutationscanbemadefromthelettersofthewordaccess=(6) .LetX1,X2,XnbearandomsampleofsizentakenfrompopulationE('),1n2X='、Xi,thenE(X)=.ni4(7) .LetXi,X2,Xnbearandomsampleofsizentakenfrompopulation22

4、S_SN(N產(chǎn)),and仃areunknown,ifx-t(k),Xt(k)isaconfidencen2'.n2intervalforwithconfidencelevel1-thenk=.ScoreQuestion2(18points)ChoosingtheonlyonerightresultSignature(1) .SupposeX-N(0,1),YN(1,1),ifXandYareindependent,then()(A)P(XY_0)=1/2(B)P(XY_1)=1/2(C)P(X-YE0)=1/2(D)P(X-Y£1)=1/2(2) .SupposeXN(3,4

5、),YE(5),findtheerrorresult()(A)EXY)=8(B)DXY)；=292,2/XY5(C)E(X2+Y2)=63(D)EX+Y-1=01252)(3) .SupposethatrandomvariablesXandYareindependent,iftheyhavethesameprobabilitydistributionwith1U/32,thenP(X=Y)=2/3；(A)2/3(B) 1(C) 1/2(D)5/9(4) .SupposeXN(,巴2),andYN(N2，。；),ifP(X-|1)P(Y-I121),then()(A)。二二(B)二二二(C):(

6、D)對(duì)：N(。二2),G21n-1n工(Xii1Oc1nc_O-X)2,S；=1<(XiX)2,S221nS：(Xini1thenthefollowingrandomvariableswhichoneisthet-distributionwithn-1degreesoffreedom.X(A)n-1§(B)X-.n-1S2(C)S3.n(D)S4(6).SupposeXP('),Y=2X5,then(A)1(B)-1(C)1/2(D)0(5).LetXiX,XnbearandomsampleofsizentakenfrompopulationScoreSignature

7、Question3:(12points)SupposearandomvariableXhasthedensityfunctionf(x)=，'2x,*0：x：1elsewhereObserveXindependentlyforthreetimes,letYdenotethenumberofaneventX:occurringinthreetimes,determine:(1) theprobabilitydistributionofY;2(2) theprobabilitydistributionofY.ScoreSignatureQuestion4(14points)Suppose(

8、X,Y)hasthejointdensityfunctionasfollows:rif(x,y)=9._一c(xy)0三x三1,0mym1elsewhere(1)Findtheconstantc;(2) AreXandYindependent?(3) DeterminetheconditionaldistributionofXforanygivenvalueofY.11p(x<2丫=2)ScoreQuestion5(10points)SignatureSupposethataboxcontainsonefaircoinandonecoinwithaheadoneachside.Suppo

9、sealsothatonecoinisselectedatrandomandtossed,aheadisobtained.Determine:(1) theprobabilityofthiseventoccurring;(2) theprobabilitythatthiscoinisthefaircoinwhentheaboveeventoccurred.第5頁(yè)共8頁(yè)ScoreSignatureQuestion6(5points)Thereare4girlsand8boystakepartininterviewofsomecompany.Supposethattheinterviewersel

10、ectonestudentrandomlyeverytime,determinetheprobabilitythattherearejust2boyswaitingforinterviewingwhenallthegirlshaveinterviewed.ScoreQuestion7(12points)SignatureJ-1x,SupposearandomvariableXhasthedensityfunctionf(x)=1-x,0-1：x.00<x_1elsewhereX：0X,0Z二,；letdetermine:(1)thejointprobabilitydistributionof(Y,Z);D(Y+Z).,where6is0,x<0ScoreSignatureQuestion8(8po