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Topic: Conditional expectation notation and the expectation of an i.i.d process
Replies: 19   Last Post: Mar 1, 2016 12:39 PM

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 Gordon Sande Posts: 137 Registered: 5/13/10
Re: Conditional expectation notation and the expectation of an i.i.d process
Posted: Feb 26, 2016 10:01 AM

On 2016-02-26 14:13:51 +0000, Tiger said:

> This is probably a simple question but I am somewhat confused.
>
> Let v_s (_s indicates time subscript) be i.i.d normal, where s = {t,
> t+1, ?, T}. Consider the expectation of v_s condition al t i.e.
> E_t(v_s).
>
> Question 1:
>
> How do I read E_t(v_s)? In particular I am a little confused about the
> subscript "_t" of the expectation operator "E". Expected value of v_s
> conditional on t. What does "conditional on t" really mean here? Does
> it mean E(v_s | v_t)? So does it mean the expected value of v_s given
> the information on v at t?
>
> Question 2:
>
> I suspect
>
> for s = t: E_t(v_t) = v_t
>
> and
>
> for s = t+1: E_t(v_t+1) = E(v_t+1)
>
> would hold if v_s is an i.i.d process. Am I right?

Where did you find this notation? There should be an explanation of its
usage there.

Notation means whatever its author claims it means, subject to its
being well formed.
Just because it can be written down does not mean it makes sense! Some
notation is so
common and so useful that it no longer is defined in its usage although
careful text
books may include explanations.

Date Subject Author
2/26/16 Bijan Mobasseri
2/26/16 Gordon Sande
2/26/16 Bijan Mobasseri
2/26/16 Gordon Sande
2/26/16 Bijan Mobasseri
2/27/16 Bijan Mobasseri
2/27/16 David Jones
2/27/16 Bijan Mobasseri
2/27/16 Bijan Mobasseri
2/27/16 Herman Rubin
2/27/16 Bijan Mobasseri
2/28/16 Guest
2/29/16 Bijan Mobasseri
2/29/16 Bijan Mobasseri
2/29/16 David Jones
2/29/16 Bijan Mobasseri
2/29/16 David Jones
2/29/16 Bijan Mobasseri
3/1/16 Nick
3/1/16 Bijan Mobasseri