雨课堂学堂在线学堂云《Probability and Mathematical Statistics（云南财经）》单元测试考核答案

第1题Mutuallyexclusiveeventsarealsoopposingevents.()第2题Opposingeventsarealsomutuallyexclusiveevents.()第3题andareagroupofdivisions,then.()第4题Letandbeanytwoevents,thendenotes().ANecessaryeventBJustoneofandhappensCImpossibleeventDanddonotoccuratthesametime第5题Byutilizingtherelationshipsbetweenevents,equationissimplifiedto()ABCD第6题Usingtherelationshipbetweenevents,theformulaissimplifiedto()ABCD第1题Theprobabilityofaninevitableeventis1.()第2题,thenisanimpossibleevent.()第3题If,andareincompatiblewitheachother,then.()第4题Ifauniformdiceisrolledtwiceinsuccession,theprobabilityoftheevent"thesumofpointsis3"is()ABCD第5题Supposethateventmustoccurwhenbotheventsandoccur,then()ABCD第6题If,and,areknown,theprobabilitythateventswillnotoccuris()ABCDExercises1.3第1题Inthetestofthrowingadice,theprobabilityofeachbasiceventis1/6.()第2题Afour-volumeanthologyisplacedonthebookshelfinanyorder,andtheprobabilityofeachvolumebeingexactly1,2,3and4fromlefttorightorfromrighttoleftis1/12.()第3题Thereare6maledoctorsand5femaledoctors,fromwhich2maledoctorsand1femaledoctorareselectedtoformamedicalteam,andthedifferentselectionmethodsare()A60B70C75D85第4题Chooseoneof10numbers,suchas0,1,...,9,etc.,andputitbackaftertakingitout.Takeitthreetimesinsuccession.Theprobabilitythatthesumofthethreenumberstakenoutisequalto15is()A0.063B0.025C0.073D0.065第5题Thereare8redballsand2whiteballsinthebox,andtheprobabilityof"gettingtworedballs"is()ABCD第6题Someoneforgetsthelastdigitofthetelephonenumber,sohedialsatwill.Theprobabilitythathedialsnomorethanthreetimesandconnectstherequiredtelephoneis()ABCDExercises1.4.1第1题Giventhateventsandareincompatiblewitheachotherand,thenprobability。()第2题If,and,then=.()第3题Given,,then=()ABCD第4题Thereare6redballsand4whiteballsin10ballswiththesameshapeandsize,and2ballsarepulledoutinturnwithoutputtingthemback.Undertheconditionofpullingouttheredballforthefirsttime,theprobabilityofpullingouttheredballforthesecondtimeis()ABCD第5题Giventhatandarerandomevents,,,,thenknownas()ABCDExercises1.4.2第1题Ifitisknownthatafamilyhasthreechildren,atleastoneofwhomisagirl,theprobabilitythatthefamilyhasatleastoneboy(assumingthattheprobabilityofhavingboysandgirlsisequal)is()ABCD第2题Giventhatthequalifiedrateofacertainbatchofproductsis0.9,theprobabilityoftheinspectormistakingthequalifiedproductsfordefectiveproductsis0.02,andtheprobabilityofadefectiveproductbeingmistakenforqualifiedproductsis0.05.Thentheprobabilityofcheckinganyproductbeingconsideredasqualifiedproductsis()A0.688B0.268C0.887D0.668第3题Itisknownthatthequalificationrateofabatchofproductsis0.9.Whentheinspectorinspects,theprobabilitythatthequalifiedproductsaremistakenfordefectiveproductsis0.02,andtheprobabilitythatadefectiveproductismistakenforqualifiedproductsis0.05.Thentheprobabilitythattheproductsthatareregardedasqualifiedproductsarereallyqualifiedis

()A0.694

B0.994C0.889D0.668第4题Therearethreeguns,,andthatfireindependentlyatatargetatthesametime.Thehitrateofeachgunis0.2,0.3,and0.5respectively.Theprobabilityofthetargetbeinghitbyoneshotanddestroyedis0.2,theprobabilityofbeinghitbytwoshotsanddestroyedis0.6,andtheprobabilityofbeinghitbythreeshotsanddestroyedis0.9.Thentheprobabilityofthethreegunsdestroyingthetargetinoneshot()A0.253B0.354C0.254D0.554第5题Therearethreeguns,,,and,whichfireindependentlyatatargetatthesametime.Thehitrateofeachgunis0.2,0.3,and0.5respectively.Theprobabilityofthetargetbeinghitbyoneshotandbeingdestroyedis0.2,theprobabilityofbeinghitbytwoshotsandbeingdestroyedis0.6,andtheprobabilityofbeinghitbythreeshotsandbeingdestroyedis0.9.Ifthetargetisdestroyed,theprobabilityofbeingshotonlybygun()A0.126B0.324C0.554D0.0554Exercises1.5第1题Ifthethreeevents,andsatisfy,then,andareindependentofeachother.()第2题Ifthethreeevents,andareindependentofeachother,then.()第3题Ifandareindependentofeachother,thefollowingeventsthatarenotindependentofeachotherare()AandBandCandDand第4题Thehitratesof,andare、andrespectively.Nowthreepeopleshootatargetonceeach,andtheprobabilityofthetargetbeinghitis()ABCD第5题andapplyforajobatthesametime.Iftheprobabilityofbeingemployedbyandis0.5and0.6respectively,andtheemploymentofthetwopeopleisindependentofeachother,theprobabilityofatmostoneofthetwopeoplebeingemployedis()A0.7B0.75C0.6D0.5第6题Lettheprobabilityoftwoindependenteventsandnotoccurringbe,andtheprobabilityofoccurringnotoccurringisequaltotheprobabilityofoccurringnotoccurring,then()ABCDExercisesforChapter1第1题()A180B250C280D330第2题Flipacointwiceindependently.Events:{Thefirsttossappearsonthefront},{Throwthesecondfront},{positiveandnegativesideappearonceeach},{positivesideappearstwice},thentheevent()AareindependentofeachotherBareindependentofeachotherCareindependentofeachotherDareindependentofeachother第3题Foranytwoeventsand,()ABCD第4题Foranytwoeventsand,whatisnotequivalenttoandequalsis()ABCD第5题Let,,,then()AEventsandareincompatiblewitheachotherBEventsandareoppositetoeachotherCEventsandarenotindependentofeachotherDEventsandareindependentofeachother第6题Letandbeanytwoevents,then()ABCD第7题Ifthereare4unqualifiedproductsin10products,taketwoofthematanytime.Ifoneofthetwoproductsisknowntobeunqualified,theprobabilitythattheotherisalsounqualifiedis()A0.2B0.3C0.6D0.5第8题Assumingthatthefirst,second,andthird-classproductsaccountfor0.6,0.3,and0.1respectivelyinabatchofproducts,ifoneofthemistakenoutatwillandtheresultisnotathird-classproduct,theprobabilityoftakingoutthefirst-classproductis(

)ABCD第9题Thetraineeusesonemachinetomanufacturethreepartsofthesamekindinsuccession,andtheunqualifiedrateofthe()partis.Ifrepresentsthenumberofqualifiedproductsinthethreeparts,then()ABCD第10题Lettheprobabilitiesofrandomevents,andtheirsumbe0.4,0.3and0.6,respectively.Iftheinverseofrepresentstheoppositeeventof,thentheprobabilityoftheproducteventintersectingtheinverseof()A0.2B0.3C0.1D0.5第11题Thereare3elevatorsonthefirstfloorofahotel,andnowthereare5peoplewhowanttotaketheelevator.Assumingthatwhichelevatoreachpersonchoosestotakeisrandom,theprobabilityofatleastonepersonineachelevator()A0.22B0.32C0.62D0.52第12题Ashootershootsthesametargetfourtimesindependently.Iftheprobabilityofhittingatleastonetimeis80/81,theshooter'shitrateis()ABCDExercises2.1第1题

IfthedistributionfunctionofXis

,Soiscontinuouseverywhereinrange

.第2题Randomvariablesareusuallydividedintodiscretetypeandnon-discretetypebytheirdifferentvalues.Themostimportantofthenon-discreterandomvariablesisthecontinuousrandomvariable.第3题

IfthedistributionfunctionofXis

.For.Ifwhichoneistrue

(

).ABCD第4题Inthefollowingfunctions,

(

)

canbeusedasthedistributionfunctionoftherandomvariableX.ABCD第5题IfthedistributionfunctionofXis,valuesofAandBare().A、B、C、D、Exercises2.2第1题Ifthenumbersofpossiblevaluesofarandomvariableisfiniteorcountablyinfinite,therandomvariableiscalledadiscreterandomvariable.

第2题IfYisusedtorepresentthenumbersofmessagesreceivedbyamobilephonewithinamonth,thepossiblevaluesofYare1,2,3…n.第3题TheprobabilitydistributionofrandomvariableX

isasfollowing.ThedistributionfunctionofXis(

).ABCD第4题

IftheabsolutevalueofrandomvariableXisnotgreaterthan1.

,.

So(

).A58B18C38D14第5题Ifashooterhasahitrateof0.4,theprobabilityofhittingthetargetafter10consecutiveshotsis(

).ABCD第6题Therearefivemultiplechoicequestionsonatestpaper.Eachquestionlistsfourpossibleanswers,onlyoneofwhichiscorrect.Theprobabilitythatastudentgetsatleastfourcorrectanswersbyguessingis(

).A164B364C1−3545D564Exercises2.3第1题ThedensityfunctionofacontinuousrandomvariableXisf(x).∫0+∞f(x)dx=1

.第2题

ContinuousrandomvariableXhavedensityfunctionf(x)anddistributionfunctionF(x).F(x)isacontinuousfunctioninrange(−∞,+∞).第3题

X

~N(0,1),andthedistributionfunctionofXis

Ф(x).Ф(-x)=1-Ф(x)第4题ThedensityfunctionofacontinuousrandomvariableXisf(x).P{X≥5}=().A∫5+∞f(x)dxB∫05f(x)dxC∫−∞5f(x)dxD−∫−∞5f(x)dx第5题LetdistributionfunctionofthecontinuousrandomvariableXbe

ThedensityfunctionofXis(

).ABCD第6题LettherandomvariableXfollowtheuniformdistributionof[1,5],

andx1<1<x2<5.P{x1<X<x2}=().ABCD第7题If,hedistributionfunctionofXisF(x)andthedistributionfunctionofthestandardnormaldistributionis.So

(

).ABCD第8题If

,(

).ABCDExercises2.4第1题Thefunctionoftherandomvariableisanewrandomvariable.

第2题

Afunctionofacontinuousrandomvariableisnotnecessarilyacontinuousrandomvariable.第3题TheprobabilitydistributionofXis

.IfY=1-X,theprobabilitydistributionofYis(

).ABCD第4题

TheprobabilitydistributionofXis.IfY

=

X2,thedistributionfunctionofYis().ABCD第5题IfX⁓U[0,2],thenthedensityfunctionofY=1-3Xis(

).ABCDExercises2.5第1题Thedistributionfunctionoftwo-dimensionalrandomvariable(x,y)isF(x,y).ThemarginaldistributionfunctionwithrespecttoXis

FX(x).FX(x)=F(x,+∞).第2题Iff(x,y)isthedensityfunctionofatwo-dimensionalrandomvariable(X,Y),thenf(x,y)³0.第3题

Iftheprobabilitydistributionoftwo-dimensionalrandomvariable(X,Y)isasfollows.ThevaluesofaandP{1≤X<2.5,2<Y≤4}are().ABCD第4题Iftheprobabilitydensityoftwo-dimensionalrandomvariable(X,Y)isasfollowing..

ThevaluesofkandP{X<1}are(

).ABCD第5题Lettheprobabilitydensityoftwo-dimensionalrandomvariable(X,Y)beasfollowing.

.

P{X+Y≤1}=(

).ABCDExercises2.6第1题IfrandomvariablesXandYareindependent,theirjointdistributioncanbeuniquelydeterminedbytheirmarginaldistributions.第2题

(X,Y)isatwo-dimensionaldiscreterandomvariable,and

(x0,y0)isavalueof(X,Y).IfP{X=x0,Y=y0}=P{X=x0}P{Y=y0},wecansayXandYareindependent.第3题Lettheprobabilitydistributionofthetwo-dimensionalrandomvariable(X,Y)beasfollowing.

IfP{Y=1|X=0}=1/2，P{X=1|Y=0}=1/3,thenvaluesofa,bandcare(

).A0.2,0.1,0.2B0.2,0.2,0.1C

0.3,0.1,0.1D

0.1,0.2,0.2第4题Letthedensityfunctionoftwo-dimensionalrandomvariable(X,Y)beasfollowing.

fX|Y(x|y)=（

）.Ax22yB2xy3C3x2y3D5x2y2第5题IftherandomvariablesXandYareindependent,,ThejointdensityfunctionofXandYisf(x,y).Whichoneisture().Af(x,y)can'tbedetermined.BCDExercisesforChapter2第1题ContinuousrandomvariableXhasdensityfunctionf(x)anddistributionfunctionF(x),F(x)=∫−∞+∞f(x)dx.(

)第2题IfX~N(m,s2),P{|X-m|<s}doesn'tchangeassincreases.

(

)第3题

IfthedistributionfunctionoftherandomvariableXisasfollowing..P{X>12}=().ABCD第4题IfX~N(2,22),andaX+b~N(0,1),thenthecorrectoneis(

).Aa=1,b=0Ba=0.5,b=-1C

a=1,b=2DThevaluesofaandbareuncertain.第5题

LetthedensityfunctionofrandomvariableXbeasfollowing.

P{X<1.5}=().A∫−∞1.5(2−x)dxB∫01.5(2−x)dxC∫11.5(2−x)dxD∫01xdx+∫11.5(2−x)dx第6题ThedensityfunctionofrandomvariableXisfX

(x).IfY=-3X+2,thenthedensityfunctionofYis

(

).

A−13fX(y+23)B13fX(y+23)C13fX(−y−23)D−13fX(−y−23)第7题Iftwoidenticaldicearerolledatthesametime,andXandYrepresentthenumberofthefirstandseconddice,then().ABCDExercises3.1第1题（（））E(X2)>（E（X））2.第2题ForanyrandomvariableX,ifE(X)exists,thenE(E(X))=E(X).

第3题IfE(XY)=E(X)E(Y),thenXandYisindependentofeachother.

第4题LetthedistributionlawofrandomvariableXbeasfollows,X012p00.50.5then

E(X2)isequalto().A1B1.5C2.5D3第5题IftheprobabilitydensityfunctionofrandomvariableXis

f(x)=2x,0<x<1;

f(x)=0,otherwise,thenE(X)isequalto().A2/3B1C3/2D8/3第6题

LetrandomvariablesXandYbeindependentofeachother,andE(X)=3,E(Y)=2,thenE(XY-Y)isequalto().A3B4C10D12Exercises3.2第1题ThevarianceD（X）ofrandomvariableXdescribestheconcentrationofX’svalues.()第2题LetXandY

beanytworandomvariables,andE(XY)=E(X)E(Y),thenD(XY)=D(X)D(Y).()第3题

LetXandYbeanytworandomvariables,thenD(X+Y)=D(X)+D(Y).(

)第4题LettheexpectationandvarianceofrandomvariableXbeE(X)=-2,D(X)=1,thenE(X2)isequalto().

A-1B1C3D5第5题WhentherandomvariableXfollowsthe(

),E(X)=D(X).A

BinomialdistributionBNormaldistributionCPoissondistributionDExponentialdistribution第6题LetthestandarddeviationofrandomvariableXbe3,thenD(-2X+2)isequalto（

）.A6B12C14D36Exercises3.3第1题IfE(XY)=E(X)E(Y),thenXandYisuncorrelated.(

)第2题IfthecorrelationcoefficientofrandomvariablesXandYisequalto0,thenXandYareindependent.()第3题Fortwo-dimensionalnormalrandomvariables(X,Y),XandYisuncorrelatedifandonlyifXandYisindependent.()第4题cov(X-Y,-Z)=（）.Acov(X,Z)-cov(Y,Z)Bcov(X,Z)+cov(Y,Z)Ccov(Y,Z)-cov(X,Z)D

TheanswersofA,BandCarenotright第5题Whichofthefollowingstatementsiswrong().AIfthecorrelationcoefficientisequalto0,thenthecovariancemustbeequalto0;

BIfthecovarianceisgreaterthan0,thenthecorrelationcoefficientmustbegreaterthan0;CIfXandYareindependentofeachother,thenXandYmustnotbeuncorrelated;

DIfcovarianceisequalto0,thenXandYmustbeindependentofeachother.Exercises3.4第1题Comparedwiththecentrallimittheorem,theestimategivenbyChebyshevinequalityismoreaccurate.()第2题

Laplacecentrallimittheoremshowsthatnormaldistributionisthelimitdistributionofbinomialdistribution.()第3题Bernoulli'slawoflargenumbersshowsthatthefrequencyofeventAconvergestotheprobabilityofeventAinprobability.

(

)第4题

LetXbetherandomvariableofbinomialdistributionwithn,p,thenwhenntendstoinfinity,P{a<X<b}≈（）.AΦ(b)+Φ(a)BΦ(b)-Φ(a)C

Φ(a)-Φ(b)D2Φ(b)-1第5题

LettherandomvariablesequencesX1,X2...,Xnbeindependentofeachother,anditobeystheuniformdistributionon[a,b],thenthemeanvalue

(X1+X2+...+Xn)/nconvergesto(

).A(a+b)/2B(b−a)2/12C(a+b)2/12D(b-a)/2ExercisesforChapter3第1题E（XE(X)）=E(X)

(

)第2题ThecorrelationcoefficientofrandomvariableXandYis0,thenXandYhasnolinearrelationship.(

)第3题Bernoulli'slawoflargenumbersshowsthatrandomeventswithverysmallprobabilitycanhardlyoccurinindividualexperiments.()第4题TherandomvariableXobeysthePoissondistributionwithparameter3.

Whichofthefollowingconclusionsiscorrect?（

）AE(X)=3,D(X)=9BE(X)=9,D(X)=3CE(X)=3,D(X)=3DE(X)=9,D(X)=9第5题GiventhatD(X)=4,D(Y)=25,andcov(X,Y)=6,thenthecorrelationcoefficientofXandYis(

)A0.06B0.6C6D60第6题IfXandYarerandomvariables,andCisconstant,thenwhichofthefollowingconclusionsiscorrect?(

)AD(X+Y)=D(X)+D(Y)BD(X+C)=D(X)+CCD(X-Y)=D(X)-D(Y)DD(X-C)=D(X)第7题

IfX∼N(1,42),thenwhichofthefollowingstatementisincorrect?（）AE(X)=1BD(X)=4CP{X=1}=0DP{X<1}=0.5第8题UsingtheChebyshevinequality,

）P{|X−E(X）|<3D(X)}≥()A1/9B1/3C8/9D1第9题TherandomvariableXobeysthebinomialdistributionwithparametern,p,thenn→∞,P{a≤X≤b}≈(

)，where∅(x)

isthedistributionfunctionofstandardnormaldistribution.A∅(b−npnp(1−p))+∅(a−npnp(1−p))B∅(b−npnp(1−p))−∅(a−npnp(1−p))C∅(b)−∅(a)D2∅(b)−1Exercises4.1第1题Letbeasamplefromanormalpopulation.Assumeandarethesamplemeanandthesamplevariance,respectively.Whichfollowingstatementsareincorrect?()ABTheexpectationofthesecondcentralmomentofthesampleisCD第2题Letbeapopulationpossessinguniformdistributionontheinterval,whereisanunknownparameter.Whichofthefollowingstatementistrue?()AisastatisticBisastatisticCisastatisticDisastatistic第3题Letbeacontinuouspopulationwithprobabilitydensityfunction.Thentheprobabilitydensityfunctionofthesample.()第4题Themeanofasampleofmeasuredresponsesisgiven.()第5题Astatisticisafunctionoftheobservablerandomvariablesinasampleandknownconstants.()Exercises4.2第1题Letbeasamplefromthepopulation.Assumeand.Whatdistributiondoespossess?()ABCD第2题Letbeasamplefromthenormalpopulation.Supposepossessesthechi-squaredistributionwith2degreesoffreedom,then().ABCD第3题Ifisasamplefromthepopulation,andisthesamplemean.Whichofthefollowingstatistichasthestandardnormaldistribution?()ABCD第4题Ifandareindependent,then.()第5题Let.Then.()Exercises4.3第1题Letbeasamplefromanormalstandarddistributionpopulation.Assumeisthesamplemeanandisthesamplevariance.Whichofthefollowingstatementsholds?()ABCD第2题Letbeasamplefromthenormalpopulation.Assumeisthesamplevariance.Whatdistributiondoeshave?().AnormaldistributionBdistributionCdistributionDdistribution第3题Letbeasamplefromthenormalpopulation.Assumeisthesamplemean.Whichofthefollowingstatementsholds?()ABCD第4题Letbeasamplefromthenormalstandarddistributionpopulation.Assumeisthesamplemeanandisthesamplevariance.Whichofthefollowingstatementsholds?()ABCDExercisesforChapter4第1题Letbeasamplefromanormalstandarddistributionpopulation.Assumeisthesamplemean.Whichofthefollowingconclusionsdoesnothold?()AandareindependentBandareindependent(if)CandareindependentDandareindependent(if)第2题Letaresamplesfromanormalpopulation.Suppose.Whatarethevaluesof和().ABCD第3题Letandbesamplesfromtwoindependentnormalpopulationand,respectively.Supposethesamplevariancesareand.What’sthedegreesoffreedomof?()ABCD第4题Assume.Then.()第5题Assume.Then.()第6题Assumeand,then.()第7题Letbeachi-squarerandomvariablewithdegreesoffreedom.Thenand.()Exercises5.1.1第1题Ifistheunknownparameterinpopulation,thenthemomentestimatorofobtainedbythemomentestimationmethodisunique.()第2题Ifisthemomentestimatoroftheunknownparameterinpopulation,andisafunctionof;thenisthemomentestimatorof.()第3题Iftheobservedvalueofasampleis0,0,1,1,0,1,thenthemomentestimateofthepopulationmeanis.()第4题Letbeasimplerandomsamplefrompopulation,andtheprobabilitydistributionofis,whereisanunknownparameterofand,thenthemomentestimatorofis().ABCD第5题LetbeasimplerandomsamplefrompopulationX,andtheprobabilitydensityofXis,whereisanunknownparameter,thenthemomentestimatorofis().ABCD第6题Let0,1,0,1,1bethesampleobservationsfromthebinomialdistributionpopulation,whereisanunknownparameter,thenthemomentestimateofis().ABCDExercises5.1.2第1题Ifisanunknownparameterinpopulation,thenthemaximumlikelihoodestimatorofobtainedbythemaximumlikelihoodestimationmethodisunique.()第2题Ifisthemaximumlikelihoodestimatoroftheunknownparameterinpopulation,andisafunctionof;thenisthemaximumlikelihoodestimatorof.()第3题Ifisanunknownparameterinpopulation,thenthemaximumlikelihoodestimatorobtainedbyusingthemaximumlikelihoodestimationmethodisalwaysthesameasthemomentestimatorofobtainedbyusingthemomentestimationmethod.()第4题Themaximumlikelihoodestimateoftheunknownparameterinthepopulationisthe()ofthelikelihoodfunction.AmaximumvalueBmaximumpointCminimumvalueDminimumpoint第5题Letbethesampleobservationvalueofpopulation,thenthemaximumlikelihoodestimatorofis().ABCD第6题LetbeasimplerandomsamplefromaPoissonpopulationwithparameter,whereistheunknownparameter,thenthemaximumlikelihoodestimatorofis().ABCDExercises5.2第1题Ifisthedensityfunctionofpopulation,andisasimplerandomsamplefrompopulation,thentheestimatorofparameterisanunbiasedestimatorof.()第2题Ifareindependentidenticallydistributedrandomvariables,and,,,thenistheconsistentandunbiasedestimatorofparameter.()第3题Assumingthatthepopulation,andisthesimplerandomsamplefrompopulation,thenamongthefollowingestimatorsof,whichisnottheunbiasedestimatorof.()ABCD第4题Assumingthatthepopulation,andisthesimplerandomsamplefrompopulation,thenamongthefollowingestimatorsof,whichisthemosteffective.()ABCD第5题Letbeasimplerandomsamplefromthenormalpopulation.Inordertomakebeanunbiasedestimatorofthepopulationvariance,then().ABCDExercises5.3.1第1题Assumingthepopulation,whereisknown,thentherelationshipbetweenthelengthofconfidenceintervalandtheconfidencelevelfofthepopulationmeanis:whenisreduced,decreases.()第2题Theconfidenceleveloftheunknownparameterforapopulationreferstotheprobabilitythatthisparameterfallsintotheconfidenceinterval.()第3题Theconfidenceintervalfortheunknownparameterofthepopulationisuniquelydeterminedwithknownsampleobservationsandgivenconfidencelevel.()第4题Assumingthepopulation,regardlessofwhetherisknownornot,thecenteroftheconfidenceintervalofthepopulationmeanis().AB0CD第5题Assumingthepopulation,whereisunknown,ifthesamplesizeandtheconfidencelevelforthepopulationmeanremainunchanged,thenfordifferentsampleobservations,thelengthoftheconfidenceintervalofthepopulationmeanbecomes().AlongerBshorterCinvariantDunabletodetermineExercises5.3.2第1题Assumingthepopulation,whereisknown,inordertoensurethattheconfidenceintervallengthofthepopulationmeanwithaconfidencelevelofbenotgreaterthan,thesamplesizeshouldbe:.()第2题Assumingthepopulation,whereisknown;thentheconfidenceintervaloftheunknownparameterwithaconfidencelevelofisnotuniquelydetermined;Ifthesymmetricintervalcenteredaroundthesamplemeanisusedastheconfidenceinterval,thenitslengthisthelongestandtheestimationaccuracyisthehighestamongalloftheconfidenceintervalsof.()第3题Assumingthepopulation,whereisknown;inordertoestimatethebilateralconfidenceintervalofthepopulationmeanwithaconfidencelevelof,thepivotvariableandthecorrespondingconfidenceintervalshouldbeselectedas().ABCD第4题Assumingthepopulation,whereisunknown;inordertoestimatethebilateralconfidenceintervalofthepopulationvariancewithaconfidencelevelof,thepivotvariableandthecorrespondingconfidenceintervalshouldbeselectedas().ABCDExercises5.3.3第1题Assumingthepopulation,,whereandareknown;thenthebilateralconfidenceintervalforthedifferencebetweenthemeanvaluesoftwopopulationswithaconfidencelevelofis.()第2题Assumingthepopulation,,whereandareunknownand;thenfortheindependentsmallsamples(,),thebilateralconfidenceintervalforthedifferencebetweenthemeanvaluesoftwopopulationswithaconfidencelevelofis.()第3题Inordertocomparetheservicelivesand(unit:hour)ofthetwotypesofimagingtubes,werandomlyselected10imagingtubeseach,andobtainedsampledataand,then,,,arecalculated.AssumethatthepopulationandYaresubjecttonormaldistribution,andtheirvariancesareequalto,thenthebilateralconfidenceintervalforthedifferencebetweenthemeanvaluesoftwopopulationswithaconfidencelevelofis().ABCD第4题Inordertocomparetheservicelivesand(unit:hour)ofthetwotypesofimagingtubes,werandomlyselected10imagingtubeseach,andobtainedsampledataand,then,arecalculated.Assumethatthepopulation,,thenthebilateralconfidenceintervalforthevarianceratiooftwopopulationswithconfidencelevelof0.95is().ABCDExercisesforChapter5第1题Letbeasampletakenfrompopulation,samplemeanandpopulationvariance,thenisanunbiasedestimatorof.()第2题Ifisthemaximumlikelihoodestimatoroftheunknownparameterinpopulation,andisafunctionof;thenisthemaximumlikelihoodestimatorof.()第3题Ifare