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Conditional Independence and Independence question

akolman

New member
Feb 2, 2012
1
Hello, I am stuck with the following question.

1. Suppose T ind. C |Z, does it follow that T ind. C ?

2. Suppose T ind. C , does it follow that T ind. C |Z?

I think both don't follow, but I don't know how to show it

Thanks in advance
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Hello, I am stuck with the following question.

1. Suppose T ind. C |Z, does it follow that T ind. C ?

2. Suppose T ind. C , does it follow that T ind. C |Z?

I think both don't follow, but I don't know how to show it

Thanks in advance
\(T\) and \(C\) independent given \(Z\) means:

\(P(T \wedge C|Z)=P(T|Z)P(C|Z)\)

Now we are free to define any relation we want between \(T\) and \(C\) if \(\neg Z\) is the case so that

\(P(T \wedge C) \ne P(T)P(C)\)

CB
 
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