I'll use X's instead
So
Thus
But each of these are the same, producing
I have problem with the following question
Let be independent and identically distributed random variables with . Show that
where
I proceed this way:
I want to know wether this is true or not.
???
Now since are independent and identically distributed, then
so finally
Same problem : http://www.mathhelpforum.com/math-he...-v-136142.html
And I don't agree with you going to this step :
equality of the expectations doesn't mean equality of the conditional expectations.
As for proving that , remember that if we have two sigma-algebras (or sigma-algebras generated by random variables) such that , then for a rv X,
now consider and and you have your equality.
(why is there the inclusion ? because if is a measurable function of and is a measurable function of )
If you don't know what a sigma-algebra is, then just forget my post