## Need to confirm my thinking on a probability problem

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

### Need to confirm my thinking on a probability problem

Hi this is a homework problem, so I am not looking for an answer. Just want to confirm my thinking is right, because this seems too simple. We are given
\xi is a random variable following the standard normal distribution. Find E\left( {\xi |{\xi ^2}} \right).
It seem given {{\xi ^2}}>0 we only have two possibilities for \xi of opposite sign with equal probability. So E\left( {\xi |{\xi ^2}} \right)=0

Am I missing something???
newbie

Posts: 33
Joined: Thu Nov 05, 2009 8:19 pm UTC

### Re: Need to confirm my thinking on a probability problem

newbie wrote:Hi this is a homework problem, so I am not looking for an answer. Just want to confirm my thinking is right, because this seems too simple. We are given
\xi is a random variable following the standard normal distribution. Find E\left( {\xi |{\xi ^2}} \right).
It seem given {{\xi ^2}}>0 we only have two possibilities for \xi of opposite sign with equal probability. So E\left( {\xi |{\xi ^2}} \right)=0

Am I missing something???
I don't think your missing anything. But that is a really weird question, maybe you should double check that you've read it correctly?

(Or maybe your professor doesn't like conditioning on events with probability zero, so if you answer the question they'll laugh at you because you should have written "undefined" or something dumb like that.)
Indigo is a lie.
Which idiot decided that websites can't go within 4cm of the edge of the screen?
There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Macbi

Posts: 941
Joined: Mon Apr 09, 2007 8:32 am UTC
Location: UKvia

### Re: Need to confirm my thinking on a probability problem

How was E(X|Y) defined for you?
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

z4lis

Posts: 706
Joined: Mon Mar 03, 2008 10:59 pm UTC

### Re: Need to confirm my thinking on a probability problem

Indirectly, assume S is a sigma algebra induced by the random variable {\xi ^2} then \int_A {\xi P\left( {d\omega } \right) = \int_A {E\left( {\xi |{\xi ^2}} \right)P\left( {d\omega } \right)} \;\forall A \in S}
newbie

Posts: 33
Joined: Thu Nov 05, 2009 8:19 pm UTC

### Re: Need to confirm my thinking on a probability problem

Right, so I believe it suffices to assume that A is of the form \xi^2 \in B for a measurable subset B of the real line. Now you want to use the symmetry of the normal distribution.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

z4lis

Posts: 706
Joined: Mon Mar 03, 2008 10:59 pm UTC

### Re: Need to confirm my thinking on a probability problem

Yep, that is the way I was viewing it. Thanks for the confirmation.
newbie

Posts: 33
Joined: Thu Nov 05, 2009 8:19 pm UTC