Re: Does the expectations inequality hold?
- From: "David Jones" <dajxxxx@xxxxxxxxx>
- Date: Wed, 25 Jul 2007 15:40:44 +0100
coolzai2003@xxxxxxxxx wrote:
Hey all,
I get a probability problem as follows.
Given
sum{i=1,...,N1}Xi=sum{i=1,...,N2}Yi,
where {Xi}/{Yi} are independent but NOT identical random variables. In
addition, N1 and N2 are random variables. Furthermore, we know that
E{Xi}<=E{Yj} for any i and j>0.
The question is that whether E{N1}>=E{N2} always holds.
Do what? What do you mean by "Given ..."?
Is it that you are asuming that there are these random variables (are you assuming that the Ns are independent of each other and of Xs and Ys?) and you want to condition on the event
sum{i=1,...,N1}Xi=sum{i=1,...,N2}Yi ?
Then which is the question ... is it for the conditional or unconditional expectations that you are wanting to know whether "E{N1}>=E{N2} always holds", where conditioning would be on the event
{sum{i=1,...,N1}Xi=sum{i=1,...,N2}Yi} .
I don't know the answer either way, but you could at least try to be clear.
.
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