In a time period between t=0 and t=900 (in seconds), an event will start.
The start time S is uniformly distributed (0,900) and the event duration is also uniformly distributed (0,900-s) depending on the start time
There is a second event that lies exactly between t=a and t=b, 0<=a<b<=900. What is the probability that these two events overlap for at least x second?
I'm thinking X as the overlap random variable and I would want to calculate P(X>=x). How should I do it?
What if the first event could happen in segment that there could be multiple start time and duration, what is the probability that it overlaps with the second one for at least x seconds?