Jobs arrive to a server as a Poisson process with a mean time between arrivals of $7\mathrm{.}6$ minutes. The service time is distributed exponentially with a mean time of $5\mathrm{.}2$ minutes.

a$)$ Find the long$-$run probability that the server is vacant. $(10$ pts$)$

b$)$ Find the long$-$run expected number in the system. $(10$ pts$)$

c$)$ Find the long$-$run average waiting time in the queue. $(5$ pts$)$

Write a VBA code to simulate a Poisson process with the following parameters: arrival rate $=\frac{3\mathrm{.}5}{?}$ hour, time $t_1=4\mathrm{.}2$ hours, time $t_2=12\mathrm{.}8$ hours. Return the expected number of arrivals during $t_1,t_2$ in cell A$1.(25$ pts$)$