I don't know the answer to Bill C.'s question about random positive integers, but I'll mention that there's a natural (and self-consistent) sense in which the average positive *rational* number is 3/2. As far as I'm aware, Bruce Reznick and I are the only people who know (or care about) this fact and the framework it comes from, but I've been curious about extending it further (e.g., what's the average positive rational between 0 and 1/2? what's the average of the squares of the positive rationals?), so maybe this forum is a good place to pursue this. I'll start by seeing if any of you can reconstruct the relevant notion of "average" given the hints that appear above (namely (a) the answer is 3/2 and (b) Bruze Reznick has worked on this). If nobody independently re-invents the theory over the weekend, I'll divulge more on Monday. Jim