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Math Help - Prove this random variables family is independent

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    Prove this random variables family is independent

    \Omega=[0,1] with its borelian subset and P the Lebesgue measure over [0,1].
    Let A_{n}=\bigcup_k]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}] , k from 1 to 2^(n-1).
    I have showed that the (A_{n}) family is mutually independent.
    Now,
    Let X_{n}=I_{A_{n}}=\sum_k I_{]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}]}, n \in N from [0,1] in {0,1} (k from 1 to 2^(n-1))

    I have to show that the random variables are mutually independent too, but I can't get there...

    Thank you for helping me
    Last edited by Babaorumi; November 1st 2009 at 12:58 PM.
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