However, what if one is interested in the distribution of relative collision speeds, aggregated over collisions?
Faster particles are more likely to collide during a given time window, because they sweep over a larger volume that can contain slow particles. I don't know whether they are more likely to collide with other fast particles. (I guess I can say that my intuition and knowledge fail me.)
Having the distribution I propose, along with a statistic on the number of collisions per time window, I could answer questions such as "What is the probability that a least one collision during time window T happens with a relative velocity above v?".
Is there a solution to this?