Consider a M/M/1 queue system, that is a single server queue in which customers arrive in according to a Poisson process of rate X > 0 and where service times are independent identically exponentially distributed with parameter pe> 0

• If the queue length is k > 1, what is the probability that the next customer arrives before the current customer's service time ends?
• Determine the distribution of the number of arrivals during one service period (recall that the service time is exponentially distributed with parameter > 0).