Suppose that $X_1,...,X_n$ are Random Variables and given that there exist an $k$ where k is an integer and $1\le k\le n-1$ s.t. the joint distribution $F_{X_1,...,X_k}$ are independent to $F_{X_k+1,...,X_n}$, prove that for all $1\le r \le k\le m\le n-1$ the joint distribution of $X_1,...,X_r$ is independent to joint distibutions $X_{m+1},...,X_n$
A question about independent random variable and probability distribution
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probability
probability-theory
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0What did you try? – 2012-10-04
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0i tried to use contradiction, but not sure how to get the contrary – 2012-10-04
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0I fail to see how a proof by contradiction would help. More to the point: what is the conclusion you try to reach, that is, what are you trying to prove? – 2012-10-04