What Does This Notation Mean in Conditional Probability?

[Cinitiator]

Homework Statement

Could anybody please explain this notation? The only thing I undersand here is the limit. Is r a superscript? If not, what is it? And what does E(variable|condition/equation) mean?

I know that in the set theory, | means a separator between the variable and condition (ex: S = {x | f(x) = 5}, but what does it mean in this case?

Homework Equations

The Attempt at a Solution

Googling.

 

[Hurkyl]

It's dealing with conditional probability; in this case, looking for the conditional expectation of X.