Homework4Dueon3/30/20181.(TextbookSection3.5-7,Page91)Supposethatthejointp.d.f.ofXandYisasfollows:f(x,y)=���2xe−y,for0≤x≤1,and0≤y≤∞0,otherwise.AreXandYindependent?2.Supposethatthejointp.d.f.ofXandYisasfollows:f(x,y)=���c(x+y2),for0≤x≤1,and0≤y≤10,otherwise.Determine(a)theconditionalp.d.f.ofXforeverygivenvalueofY,and(b)Pr(X<12|Y=12).3.(TextbookSection3.7-7,Page108)Supposethatthep.d.f.ofarandomvariableXisasfollows:f(x)=���1n!xne−x,forx>00,otherwise.SupposealsothatforanygivenvalueX=x(x>0),thenrandomvariablesY1,...,Ynarei.i.d.andtheconditionalp.d.f.gofeachofthemisasfollows:g(y|x)=���1x,for000,forx≤0.Findthep.d.f.ofY=X1−X2.6.LetWdenotetherangeofarandomsampleofnobservationsfromauniformdistri-butionontheinterval[0,1],DeterminethevalueofPr(W>0.9).2
