Well, there are distributions which don't have well defined expected value and I agree that it's valuable lesson. I would argue though that this is not the best

Well, there are distributions which don't have well defined expected value and I agree that it's valuable lesson. I would argue though that this is not the best example to show it. The point of two envelope problem comes much earlier and specifically giving distribution defined by you would make it completely different problem and assuming it in original form would already be a mistake. I think there are better examples to show how infinite sums and relying on expected value based on those might leads to problems. Like this one for example: http://plato.stanford.edu/entries/paradox-stpetersburg/ http://plato.stanford.edu/entries/paradox-stpetersburg/