概率论与数理统计英文题目

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1、Test1.ConsiderthesetwithsubsetsFindthefollowingsets:(a)and(b)and2.ShowDeMorgansLaw:(a),(b)3.(a)LetP(A)=0.5,P(B)=0.4,P(A∩B)=0.2.FindP(A∪B)andP(A

2、B)(b)ConsidertwofairdiceAandB.DieAissix-sidedandisnumbered1throughto6whilstdieBisfour-sidedandisnumbered1through4.Bothdicearerolled.Fi

3、ndtheprobabilityoftwodiceshowthesamescore.4.(a).LetXbearandomvariable..Showthat(b)ThepmfofarandomvariableXwhichhasaPoissondistributionwithparameter2.FindP(X=3).5.Suppose(X,Y)bebivariatenormaldistribution..FindthecorrelationcoefficientofXandY.6.(a)LetXUniformlydistributedon(-1,1

4、),i.e.X~U(-1,1).FindtheExpectationandVarianceofX.(b)LetXandYbecontinuousrandomvariableswithjointpdfLetZ=X+Y,Find.Inparticular,ifXandYareindependent,FindfX*fY..7.(a)TherandomvariableXhaspmfis:X0123PX(x)0.20.160.410.23FindP(1≤X<3)andFX(1.7).(b)LetXbeacontinuousrandomvariablewithp

5、dfFindP(X=3),P(X>1)and.8.Xiscontinuousr.v.withpdfLet,FindE(Y)59.LetXbeacontinuousrandomvariablewithprobabilitydensityfunction(a)FindP(1

6、XandY.(b)Determinewhetherthetworandomvariablesaredependentorindependent.11．SupposetherandomvariableXhasthedensityfunctionFindtheprobabilitydensityfunctionoftherandomvariableY=X+4.12.Takeoutanumberfrom1-200(200naturalnumbers).Find(a)theprobabilitythatthisnumbercanbedrivedby6;(b)

7、theprobabilitythatthisnumbercanbedrivedby6aswellas8.13.Threechildrenareselectedatrandomfromagroupoffiveboysandthreegirls.(a)Whatistheprobabilitythatallthreeareboys?(b)Whatistheprobabilityatleasttwogirlsareselected?14.(a)Let(b)Let，，.Find.15.(a)SupposeA,Baretwoevents,andP(A)=1/4,

8、P(B)=1/2,P(AB)=1/9,thenevaluate(b)UseBayes’TheoremtoshowthatifP(A),P(B)>0andthen16.(a)LetXhasaBinomialdistributionwithparametersnandp,i.e.X~b(n,p).Find(b)Showthat517.SupposethedistributionfunctionofarandomvariableXis，Find(a)theprobabilitythatXgetsvaluewithin(0.3，0.7);(b)thedens

9、ityfunctionofX18.TheoperationallifetimeX,inyears,ofaba