Chapter 3 Multivariate Random Variables 多元随机变量.ppt

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1、Chapter3MultivariateRandomVariables1.n-dimensionalvariablesnrandomvariablesX1，X2，...,Xncomposean-dimensionalvector(X1,X2,...,Xn),andthevectorisnamedn-dimensionalvariablesorrandomvector.2.JointdistributionofrandomvectorDefinefunctionF(x1,x2,…xn)=P(X1≤x1,

2、X2≤x2,...,Xn≤xn)thejointdistributionfunctionofrandomvector(X1,X2,...,Xn).3.1Two-DimensionalRandomVariablesDefinition3.1-P53Let(X,Y)be2-dimensionalrandomvariables.DefineF(x,y)=P{Xx,Yy}thebivariatecdfof(X,Y).TheJointcdfforTworandomvariablesGeometricinter

3、pretation：thevalueofF(x,y)assumetheprobabilitythattherandompointsbelongtoareaindarkFor(x1,y1),(x2,y2)R2,(x1

4、robabilitythat(X,Y)standsinareaG.AnswerJointdistributionF(x,y)hasthefollowingcharacteristics:(1)Forall(x,y)R2,0F(x,y)1,(2)MonotonicallyincrementforanyfixedyR,x1

5、R,yR,(4)forall(x1,y1),(x2,y2)R2,(x1

6、,Y)isFindthevalueofA，B，C。FindP{0

7、nctionsuchthatforanypoints(xi,yj),P{X＝xi,Y＝yj,}＝pij，(i,j＝1,2,…).Thatis(X,Y)～P{X＝xi,Y＝yj,}＝pij，(i,j＝1,2,…)，XYy1y2…yj…p11p12...P1j...p21p22...P2j...pi1pi2...Pij...........................Characteristicsofjointdistribution:pij0,i,j＝1,2,…；(2)x1x2xiThejointd

8、istributioncanalsobespecifiedinthefollowingtableExample2.Supposethattherearetworedballsandthreewhiteballsinabag,catchoneballfromthebagtwicewithoutputback,anddefineXandYasfollows:Pleasefindthejointpmfof(X,Y)XY1010Continuous