Let $A$ and $B$ be independent continuous random variables with supports $ \left( -\infty ,\infty \right) $ and $r$ be a continuous function. In addition, $A+B$ and $r\left( 2A+B\right)$ are independent. Is there a non-constant function $r$ and random variables $A$ and $B$ that satisfy these conditions?
3
-
1$\begingroup$ try math.stackexchange.com/questions?page=2&sort=newest $\endgroup$– Will JagyCommented Jan 25, 2012 at 5:29
-
$\begingroup$ Will: why do you suggest (the second page of) math.stackexchange.com for this question? I don't yet see the answer - instinct tells me it should be no, but I would be glad to see it answered here. Am I missing something obvious? $\endgroup$– James MartinCommented Jan 25, 2012 at 11:36
-
$\begingroup$ Will, thank you for the link, I looked there but did not find anything related to my question. James, thanks, I too think the answer should be "no" but no luck proving it. $\endgroup$– problemathCommented Feb 2, 2012 at 0:02
Add a comment
|