Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $X_{m+1},...,X_n$

share|cite|improve this question
What did you try? – Did Oct 4 '12 at 13:54
i tried to use contradiction, but not sure how to get the contrary – Mathematics Oct 4 '12 at 14:04
I 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? – Did Oct 4 '12 at 16:59

You could try to use the fact that if $X$ and $Y$ are independent random variables, and if $f$ and $g$ are two (measurable ...) functions, then also $f(X)$ is independent from $g(Y)$.

share|cite|improve this answer
but here is about the the joint pmf not pmf of a random variable – Mathematics Oct 8 '12 at 8:36
kjetil: +1. $ $ – Did Oct 8 '12 at 10:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.