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Thread: Mutual independence -> Conditional independence ?

  1. #1
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    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. #2
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    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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