Hallo,
are iid random variables with a lognormal distribution.
Am I right, that
where
are also independent?
Thanks in advance!
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...
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.
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 ?