The avarage age problem

Hi Guys,
I’m trying to figure out a good model for modeling the average age of a population. More specifically the average number of years people have been enrolled at a university who are in turn members of a club, which I call “age”.

• The rate at which new members arrive could be modeled as a poisson process with intensity 2/yr.
• The number of years each new member has already been to the university, as he becomes a member is U(1,4)
• Each member gets kicked out as he reaches the end of year 5.

I wanted to calculate the average age (in university years) of the members of the club. I have simulated it in matlab but im still trying to figure the analytical answer out. All help much appreciated!