with its borelian subset and P the Lebesgue measure over [0,1].
Let , k from 1 to 2^(n-1).
I have showed that the family is mutually independent.
Now,
Let 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 01:58 PM.
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Prove this random variables family is independent ![\Omega=[0,1]](http://www.mathhelpforum.com/math-help/latex2/img/ce8f2b74805d376533d637cdccc0e33a-1.gif "\Omega=[0,1]")
![A_{n}=\bigcup_k]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}]](http://www.mathhelpforum.com/math-help/latex2/img/a423db156ef40ed68418404d1dcb867d-1.gif "A_{n}=\bigcup_k]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}]")
![X_{n}=I_{A_{n}}=\sum_k I_{]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}]}, n \in N](http://www.mathhelpforum.com/math-help/latex2/img/1845d60d92adeeb371cfaaaa2226dd1f-1.gif "X_{n}=I_{A_{n}}=\sum_k I_{]\frac{2(k-1)}{2^n},\frac{2k-1}{2^n}]}, n \in N")
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