I have problem in the following question
Let be a sequence of independent identically distributed random variables with .
Show that the sequence with
is a martingale.
I need to prove
It can be decomposed as
Anybody could help to bring
I have problem in the following question
Let be a sequence of independent identically distributed random variables with .
Show that the sequence with
is a martingale.
I need to prove
It can be decomposed as
Anybody could help to bring
Hello,
Since is a constant, we can pull it out from the conditional expectation and we get
Since is a sequence of independent rv's, and are independent, and so is (since it's a measurable function of .
Thus we have and since the have the same distribution, these two expectations are equal...