若某路口每月(以30天计)发生车祸之次数为波以松分布

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1、八十九學年度第二學期統計學(二)Mid-termExam(C卷)21/06/28一、MultipleChoiceandTrue/False(9%,3%each):1.Ifthemeanandvarianceforthepopulationare900and9respectively,whatarethemeanandvarianceofthesamplemeanifthesamplesizeis16?a.900,144b.900,0.5625c.900,1296d.900,92.Arandomsampleofsize100isdrawnfromabinomialdistributionwith

2、mean32andvariance16.Whatisthedistributionof?a.Normalwithmean32andvariance1.6b.Normalwithmean0andvariance1c.Binomialwithn=64andp=0.5d.Noneoftheabove3.Xisdistributedwithm=10ands2=4.Yisdistributedwithm=50ands2=100.Whichonehashighercoefficientofvariation?a.Xb.Yc.thesamed.couldn’ttell二、ShortAnswer:(21%)1

3、.(6%)若某路口每月（以30天計）發生車禍之次數為波以松分布，平均次數為6次，則該路口發生車禍之間隔時間為________分布，平均間隔時間為_________天。2.(3%)ListtheformulaforChebyshev’sInequality:3.(3%)Ifsamplemean=100,samplestandarddeviation=10,andsamplesize=16,whatisthestanderrorofthesamplemean?_____________________________________________4.(6%)某電子公司生產一產品，該產品之電阻值呈

4、常態分布(m=100W,s=10W)a.試問該產品一批(10,000個)，約有多少個超過120W？__________________b.隨機抽樣25個，其平均電阻值小於96W之機率為多少？_______________5.(3%)Arandomsampleof36observationshasbeendrawnfromanormaldistributionwithmean50andstandarddeviation12.Theprobabilitythatthesamplemeanisintheinterval[47,53]is__________.三、3八十九學年度第二學期統計學(二)Mi

5、d-termExam(C卷)21/06/28OpenQuestion:(70%)1.(15%)Assumethatonehas2independentrandomsamplesofsizesn1,n2fromthesamepopulation.Showthatisabetterestimatorformthan.2.(15%)請說明:a.中央極限定理;b.大數法則;c.常態分布之標準化。3.(10%)LetXbearandomvariablewiththefollowingprobabilitydistribution:Findthemaximumlikelihoodestimatorofa,

6、basedonarandomsampleofsizen.3八十九學年度第二學期統計學(二)Mid-termExam(C卷)21/06/281.(15%)Thefollowingdataarethetemperaturesofeffluentatdischargefromasewagetreatmentfacilityonconsecutivedays:434751485250464945524651444946514945445048504950a.Calculatethesamplemeanandsamplevariance.b.Constructastem-and-leafplotofth

7、edata.c.Constructaboxplotofthedataandcommentontheinformationinthisdisplay.2.(15%)Showthatisabiasedestimatorofs2.Inaddition,whatisthebiasofthisestimator.3