Recall that an M/M/1 queueing system is a GI/G/1 system in which there is one server, customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/µ. For...

Recall that an M/M/1 queueing system is a GI/G/1 system in which there is one server, customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/µ. For anM/M/1 system, each time a customer arrives at or a customer departs from the system, we say that a transition occurs. For a fixed t > 0, let A be the event that there will be no transitions during the next t minutes. Let B be the event that the next transition is an arrival. Show that A and B are independent. Note that this phenomenon might be counterintuitive.