Er and Hr queues - compulsory test

1. Consider an Erlang-3 server, with mean service time x=1/mu. Give the variance, the second moment and the coefficient of variation of the service time.  You look at the system at a random point of time and  see that a customer is served in the second service stage. What is the expected remaining service time of this customer?

2. Consider a Hyperexponential-2 server, with parameters alpha_1=alpha_2=0.5, mu_1=2 and mu_2=1. Give the variance, the second moment and the coefficient of variation of the service time.  You look at the system at a random point of time and  see that a customer is served in server 1. What is the expected remaining service time of this customer?