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1、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…………试卷装订线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学院满分100得分………………Φ)0(=,5.0Φ)1(=.08413,Φ.1(645)=.095,Φ.1(96)=.0975,Φ)2(=.09772,Φ.2(327)=.099,Φ.2(567)=.0995,试卷所需的查表数据专业得分I.Fillintheblanks(3′×10).班级1.
2、Put3ballsinto4boxesrandomly.Theprobabilityofthatthereisatmostoneballineach装订线内不要答题，不要填写考生信息………………试卷装订线boxis；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学号3.SupposeXhasaPoissondistributionwithλ=,1then
3、P{X=E(X)}=；224.SupposeX~N(μ,σ)andtheprobabilityofthaty+4y+X=0hasnorealrootis0.5.thenμ=；一维离散型和连续型随机变量概率分布，常见分布⎧−2(x+y)>>2e,x,0y05.Suppose(X,Y)hasf(x,y)=⎨，thenP{}Y≤X=；二维⎩0,otherwise6.SupposethatX~N(0,1),Y~U(0,1),andAandBareindependent.ThenD(X-2Y+4)=；7.S
4、upposethatXandYhavethesamedistributionandX~B(201.0,),ρXY=,5.0then姓名D(X+Y)=；数字特征的计算：常见分布的期望和方差，计算性质28.SupposethatthatX1,X2,…,X6isarandomsamplefromX~N1,0().Y=(X1+X2+X3)22+(X+X+X)andcYhasaχdistribution.Thenc=；抽样分布4569.SupposethatX1,X2,X3,X4isarandomsampl
5、efromX~E(λ)andT=α(X1+X2+X3+X4)−1istheunbiasedestimator.ofλ.Thenα=；无偏估计的概念…………2210.SupposethatX1,X2,…,XnarearandomsamplefromX~N(μ,σ)andμ,σareunknown.Theconfidenceintervalforμiswithconfidencecoefficient1−α..区间估计1得分II.(01′)Inacity,50.2percentofthepeoplea
6、remenand49.8percentofthepeoplearewomen.Recordsshowthattheprobabilitythatamanhasacertaindiseaseis0.05andtheprobabilitythatawomanhasthediseaseis0.01.Ifapersoninthecityisselectedatrandom,a)findtheprobabilitythathehasthedisease.b)findtheprobabilitythatthe
7、personisawomangiventhatthepersonisfoundtohavethedisease.全概率公式及贝叶斯公式要求：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得分III.(10′).Supposethatthep.d.f.ofarandomvariableXisasfollows:⎧πAcosx,
8、x
9、≤⎪f(x)=⎨4π⎪,0
10、x
11、>⎩4⎧π⎫a)Findthevalueofthecon
12、stantAandP⎨0
