Consider a B&D queuing system which has a finite number of states denoted by n $=0,1,2,3,4.$ The arrival rates are $\backslash$lambda n $=4$ n for n $=0,1,2,3.$ The service rates are $\backslash$mu n $=$ n for n $=1,2,3,4.$ Both rates are expressed using the same time unit such as arrivals and services per week. $($b$)$Calculate the steady$-$state probabilities$\{$Pn$\}$of the system states using the general approach discussed in class, as well as in the textbook. Determine the expected queue length, the expected arrival rate, and the expected waiting time.