Hallo,

are iid random variables with a lognormal distribution.

Am I right, that

where

are also independent?

Thanks in advance!

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- June 25th 2011, 02:40 PMJujufunction of iid random variables also independent?
Hallo,

are iid random variables with a lognormal distribution.

Am I right, that

where

are also independent?

Thanks in advance! - June 25th 2011, 03:13 PMMooRe: function of iid random variables also independent?
Hello,

Yes, just use the definition of independence : X and Y are independent iff for any *correct* functions f,g, E[f(X)g(Y)]=E[f(X)]E[g(Y)]

*correct* in the sense that the expectations are defined for such functions. That would be measurable and bounded for the simplest situation I guess... - June 25th 2011, 03:32 PMJujuRe: function of iid random variables also independent?
Thank you!

I didn't know this definition. - June 25th 2011, 10:20 PMGuyRe: function of iid random variables also independent?
You can also prove that

where the are arbitrary 1d Borel sets. This implies independence from a different starting place; all my references use a different definition of independence than Moo's, but they are equivalent. - June 25th 2011, 10:55 PMJujuRe: function of iid random variables also independent?
Thank you. So if I show it this way, I just need the inverse function and use the independence of and then it follows.

Am I right?

Doesn't it matter that my function is just defined for and the inverse function for ? - June 26th 2011, 08:12 AMGuyRe: function of iid random variables also independent?
- June 26th 2011, 11:37 AMJujuRe: function of iid random variables also independent?
my function is continous (on ) and thus measurable. right?

- June 26th 2011, 11:45 AMGuyRe: function of iid random variables also independent?
Heh, you have to try much harder than that to cook up a function that isn't measurable :) Continuity is more than enough.