Hello,

I have to show the following assertion:

I know that

and

and for we have

Unfortunately I have no idea how to show it.

Does anyone have a hint?

Thanks in advance!

Printable View

- April 17th 2013, 09:51 AMJujufunction of expectation
Hello,

I have to show the following assertion:

I know that

and

and for we have

Unfortunately I have no idea how to show it.

Does anyone have a hint?

Thanks in advance! - April 17th 2013, 10:18 PMchiroRe: function of expectation
Hey Juju.

One idea I have is to use Jensens Inequality since you are dealing with a convex function log(x):

Jensen's inequality - Wikipedia, the free encyclopedia - April 18th 2013, 12:06 AMJujuRe: function of expectation
Thanks Chiro.

But I don't think that Jensen's inequality helps (or at least I don't know how):

since And that is what I already know.

Or did I anything wrong? - April 18th 2013, 12:56 AMchiroRe: function of expectation
Doesn't that mean that log of that term is <= 0 though?

- April 18th 2013, 01:45 AMJujuRe: function of expectation
Of course you are right. But anyway I think that I cannot conclude that

since the inequality does not imply

Am I right? - April 18th 2013, 02:37 AMchiroRe: function of expectation
It is just an inequality: If you know that the value is zero then it is zero.

The inequality just gives a possible range without knowing any more information: now you can add your other piece of information to reduce the inequality even further. - April 18th 2013, 02:52 AMJujuRe: function of expectationQuote:

It is just an inequality: If you know that the value is zero then it is zero.

But I think I can show it quite easily; just using

Thank you.