I have $N$ boxes with a given number of balls among the boxes. I know the occupancy distribution so I have the average number of balls per bins (let's call it the mean).
The underlying process is that at every time step we can add or remove a balls from one bins according to a given rule.
So during the process the average occupancy fluctuates (i.e. the mean has a variance and a distribution)
Is that possible to determine a connection between the the variance of the mean and the variance of the original occupancy distribution?