Problem $1(10$ pts$)($PLEASE GO THROUGH AND SHOW WORK$)$

Consider the following single$-$server queue: the inter$-$

arrival time is a Poisson distribution with a mean of $10$

minutes and the service time is exponentially

distributed with a mean of $8$ minutes,

Questions to Answer:

mean wait in the queue,

mean number in the queue,

the mean wait in the system,

mean number in the system and

proportion of time the server is idle.