There have already been a few questions on the relationship among stats.SE, math.SE, and MO.
The distinction that MO is generally reserved for higher level questions is often made, however, there is, of course, a gray area for "high level."
I also posted this question on meta: Is it acceptable to post the same question on multiple sites which received a resounding "No!"
However, the audiences on each do appear to be different. The probability tag on math.SE has 110 followers, and the probability tag on stats.SE has 17 followers (and I can't find a number on the pr.probability tag on MO). The "high users" on each don't appear to have much overlap.
So, out of etiquette, one should only post on one site at a time. But if it is a question that is equally valid on all sites, it is more likely to get answered if more people are exposed to it.
So, my questions are: is there a way you can migrate your own question from one site to another if it hasn't been answered? If so, what is the appropriate time frame to wait for an answer on the first site? If not, is it appropriate to delete the original question entirely from the first site and then re-post it on another site? I don't want to remove a question that people might find interesting, esp. if it's gotten comments and interest. But I would like to expose it to a wider audience if necessary.