Give an example for a mapping from the sample space toRthat is not a valid random variable.

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- October 31st 2013, 12:49 PMawais100not a valid random variable
Give an example for a mapping from the sample space to

*R*that is not a valid random variable. - October 31st 2013, 01:29 PMSlipEternalRe: not a valid random variable
What is "the sample space"? Is it just an arbitrary sample space ? What do you mean an example for a mapping that is not a valid random variable? Valid in what sense?

From what I gather from your question, I assume you mean that is some set, and is the smallest -algebra containing . You are looking for a map such that there exists a set such that is measurable, is not in . Is that what you mean? - October 31st 2013, 01:39 PMawais100Re: not a valid random variable
yes, what you assumed is absolutely correct. I want an example for this. I think if I assume a set that is not a field or that does not contain all subsets of Omega (Whole set), may be then I can prove that mapping of this set to R will not result in a random variable...

- October 31st 2013, 02:26 PMSlipEternalRe: not a valid random variable
Define a relation by if and only if . Show that is an equivalence relation. Then, partition by . Choose a representative from each partition where is the representative chosen from the part containing . Define a function by . That should do it.