I have the following problem: A trial of an experiment can yield a "successful" event which lasts for 10 seconds with probability 0.1. The experiment is repeated every 3 seconds. If it yields a successful event while the 10 seconds of a previous one still haven't expired, it will just renew the timer to 10 again. The question is, how should the uptime of the successful event over the course of 60 seconds be modeled? I was thinking the following: There are 20 experiments over the course of 60 seconds, and since this is a Bernoulli experiment in a way, the mean number of successes will be n*p, i.e. 2 and their uptime is 10 each, thus 20/60 = 1/3 of the time. But then again, I am not sure if this takes into consideration the possibility that a successful event will renew the timer of a successful event that happened less than 10 seconds before. Any ideas how exactly to model the uptime of the successful event from this experiment?