# Thread: Mutual independence -> Conditional independence ?

1. ## Mutual independence -> Conditional independence ?

hi, all!

I have the following question about relations between conditional independence and mutual independence:

Does Mutual independence imply Conditional independence, e.g. if X,Y,Z are mutually indepdendent, does it mean that X,Y are conditionally independent on Z?

The other question is more concrete: can the following hold:

P(A,B) = P(A)*P(B) //eg A and B independent
P(A|C) \ne P(A) //eg A is not independent of C
P(C|B) \ne P(C) //eg C is not independent of B

my intuition sais that no, since A depend on C and B depend on C, and because of that they can not be independent, but it would be nice to have a rigorous proof.

2. ## Re: Mutual independence -> Conditional independence ?

You haven't shown any work on the first one so I'll let that be for the time being.

For the second one I would say that maybe you shouldn't trust your intuition too much here. Keep on thinking about it and let us know what you come up with.

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