Natural definition for variance?

[spitz]

Homework Statement

I'm trying to find a natural definition for V[X|Y], but I'm not sure what a natural definition is. Any help?

 

[kai_sikorski]

This already has a definition. It's the second moment of X where you integrate against the pdf condition on Y. I guess I'm confused about your question.

 

[kai_sikorski]

Actually I'm assuming that you're asking about V[X|Y = y] which is just a deterministic value. The way you wrote it V[X|Y] would actually be a random variable itself. Look at the second bullet here:

http://en.wikipedia.org/wiki/Conditional_expectation#Discussion