I don't know if it is in anyway randomized. But I am pretty sure we can rule out the "tailored to title/body text" alternative.
When I visit the "Ask Question" page I always see "integral, matrices, number theory" suggested (at least I tried it a few times just now). It doesn't matter what I typed in the title and body boxes, nor does it matter whether I typed in those boxes at all.
The above experiment however doesn't rule out possibilities that
- The prompt text could be user specific; so you see something from what I see.
- The prompt text changes over time
- The prompt text is not random: it can be generated by a deterministic algorithm.