You wait in a queue served by one assistant. When you enter the queue, the assistant is serving one customer, and another customer is already waiting. The service of one customer has Exponential distribution, with a mean of 1 minute. What is your expected waiting time and what is the distribution of your waiting time?
My approach to this is as follow:
As one is in service and one is in waiting so before our service we will see 2 other services.
Expected waiting time $ = 2*Exp(\mu) = 2-minutes$
Now how to calculate the distribution of waiting time as we have two exponentially distributed services for two customers and the sum of exponential random variables is not exponentially distributed?
Also I don't have arrival rate $\lambda$ here