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Let $Y_1,..,Y_n$ be random variables. Given that for all $1\le k \le n-1,k\in \mathbb{N}$, $Y_k$ is independent to the joint distribution of the other $n-1$ random variable, prove that $Y_n$ is also independent of the other $n-1$ random variables. I have tried to show that all $Y_1,...,Y_{n-1}$ are independent but not sure how to show that even $Y_n$ are independent of joint distributions $Y_1,...,Y_{n-1}$.

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    What happened to this question?2012-10-29

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