Mean time between independent events

[Ashiataka]

Suppose I have two atoms that independently emit alpha particles. I want to find the mean $$\Delta T$$ for the events. I then want to extend this for 3, 4 etc. atoms however what I'd like to do for more than 3 atoms is find the smallest delta T for any two emissions.

What should I look at to solve this?

Thank you.

 

[Stephen Tashi]

Perhaps the Erlang distribution is relevant. http://en.wikipedia.org/wiki/Erlang_distribution