For the scheme M/M/1, show that the mean length of the queue, given that the server is busy, is equal to the mean number of particles in the system. Argue that the answer is not so surprising as it looks at first glance, showing that this is a special property of the process we consider. (Advice: Regarding, the last question, assume that the conditional expectation mentioned equals the mean number of particles in the system, and show that in this case, both are equal to (1−π₀)/π₀, which is consistent with (2.1.4).)