武汉理工大学概率论与数理统计英文版试题

…………试卷装订线………………装订线内不要答题，不要填写考生信息………………试卷装订线…………学院专业班级学号姓名武汉理工大学考试试卷（A卷）2010~2011学年1学期概率论与数理统计课程时间120分钟56学时，3学分，闭卷，总分100分，占总评成绩80%2011年1月5日题号一二三四五六七八九十合计满分100得分,995.0)567.2(,99.0)327.2(,9772.0)2(,975.0)96.1(,95.0)645.1(,8413.0)1(,5.0)0(=Φ=Φ=Φ=Φ=Φ=Φ=ΦI.Fillintheblanks(3′×10).1.Put3ballsinto4boxesrandomly.Theprobabilityofthatthereisatmostoneballineachboxis；古典概率的计算2.SupposeAandBareindependent,andP(A)=0.6andP(A+B)=0.8.ThenP(BA)=；由事件的关系和运算以及概率的性质等计算事件的概率3.SupposeXhasaPoissondistributionwith,1=λthen{}==)(XEXP；4.Supposeandtheprobabilityofthathasnorealrootis0.5.then),(~2σμNX042=++Xyy=μ；一维离散型和连续型随机变量概率分布，常见分布5.Supposehas，then),(YX⎩⎨⎧=+−otherwiseyxeyxfyx,00,0,2),()2({}=≤XYP；二维6.SupposethatX~N(0,1),Y~U(0,1),andAandBareindependent.ThenD(X-2Y+4)=；7.SupposethatXandYhavethesamedistributionand,5.0),1.0,20(~=XYBXρthen=+)(YXD；数字特征的计算：常见分布的期望和方差，计算性质8.SupposethatthatX1,X2,…,X6isarandomsamplefromandhasadistribution.Then).1,0(~NX2321)(XXXY++=2654)(XXX+++cY2χ=c；抽样分布9.Supposethatisarandomsamplefrom4321,,,XXXX)(~λEXand)(4321XXXXT+++=αistheunbiasedestimator.of.Then1−λ=α；无偏估计的概念10.SupposethatX1,X2,…,XnarearandomsamplefromX~andareunknown.Theconfidenceintervalfor),(2σμN2,σμμiswithconfidencecoefficient1.α−.区间估计得分试卷所需的查表数据1II.(Inacity,50.2percentofthepeoplearemenand49.8percentofthepeoplearewomen.Recordsshowthattheprobabilitythatamanhasacertaindiseaseis0.05andtheprobabilitythatawomanhasthediseaseis0.01.Ifapersoninthecityisselectedatrandom,a)findtheprobabilitythathehasthedisease.b)findtheprobabilitythatthepersonisawomangiventhatthepersonisfoundtohavethedisease.全概率公式及贝叶斯公式)01′要求：1.必须要设事件2.将题目所给的数据用概率的形式给出来3.要有公式详细过程见exercise3，习题课里每个题目都写了详细的过程III.().Supposethatthep.d.f.ofarandomvariableXisasfollows:01′⎪⎩⎪⎨⎧≤=4||,04||,cos)(ππxxxAxfa)FindthevalueoftheconstantAand⎭⎬⎫⎩⎨⎧60πXP;b)FindthedistributionfunctionF(x)ofX.一维连续型随机变量的分布，详见exercise6的2、3两题得分得分2IV.()Supposethatthelengthoflifeofacertainelectricalcomponenthasanexponentialdistributionwith100hourasitsmean.Randomlytaking16suchcomponentsnow,whatistheprobabilitythatthetotallengthoflifeofthesecomponentsismorethan2000hours?(UsetheCentralLimitTheorems)01′利用中心极限定理计算，详见exercise12，参考答案已经上传在参考资源里要求：1.要设变量2.用中心极限定理是近似计算，要用≈V.()SupposeDeterminethep.d.f.of.01′),2(~EXXeY21−−=随机变量函数的分布这部分内容上过习题课，exercise7再次强调：一定要用分布函数法求解VI.()GiventhatXandYhavethefollowingdistribution：01′X-101Y01p1/41/21/4p1/21/2and.a)Findthejointdistributionof1}0{==XYP()YX,;b)DeterminewhetherornotXandYareindependent.二维离散型随机变量的联合分布、边缘分布、条件分布和独立性的判断得分得分得分3VII()SupposethatXhasthefollowingdistribution：01′X123p2θ)1(2θθ−2)1(θ−wheretheparameter)10(θθisunknown.Giventheobservedvalue,2,112==xx13=x,determinethemomentestimatorsandthemaximumlikelihoodestimatorofθ.点估计，详见exercise14，参考答案已经上传在参考资源里VIII.(1)Itisclaimedthatanautomobileisdrivenontheaveragelessthan20000kmperyear.Totestthisclaim,arandomsampleof100automobileownersareaskedtokeeparecordofthekmtheytravel.Wouldyouagreethisclaimiftherandomsampleshowedanaverageof23500kmandastandarddeviationof3900km?Usea0.01levelofsignificance.0′单个正态总体均值的假设检验，详见exercise15，参考答案已经上传在参考资源里…………试卷装订线………………装订线内不要答题，不要填写考生信息………………试卷装订线…………得分得分45