I'm studying a particular system but to ease the understanding let me take a general approach. 1) Suppose I have a system comprised of N=10^10 elements. Assuming now that I deal a damage to a random element for every timestep, I want to figure out how the damages are distributed in the elements. My hypothesis is that this binomial distribution can be approximated very well by an easier poisson distribution. And this brings me to my first question: Is this a correct hypothesis? 2) Next: Now the above does not really have anything to do with the system I study. Because in my system it is so that the probability of dealing damage to an element is not uniformly distributed but rather something specific to each element (normally distributed). I want to be able to predict how the damages will be distributed amongst my elements, like in 1) but this time I'm not sure how to approach the problem. Can I predict a distribution and how would I do that?