Stat/219Math136-StochasticProcessesNotesonSection4.1.21Independence,Un - PDF document

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Uploaded On 2015-11-23

Stat/219Math136-StochasticProcessesNotesonSection4.1.21Independence,Un - PPT Presentation

Counterexample3IEXjYIEXdoesnotimplythatIEYjXIEYLetnf101gwithIPfg13for2nConsiderYandXIf0gThenIEY0andIEYjX0If0g112112If11g0soIEYjXIEY ID: 203367

Counterexample3:IE(XjY)=IE(X)doesnotimplythatIE(YjX)=IE(Y)Let\n=f1;0;1gwithIP(f!g)=1=3for!2\n.ConsiderY(!)=!andX(!)=If0g(!).ThenIE(Y)=0andIE(YjX)=0If0g(!)+(11=2+11=2)If1;1g(!)=0 soIE(YjX)=IE(Y).

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