Consider a facility with 4 machines and one person who repai

Consider a facility with 4 machines and one person who repairs machines when they fail. Suppose that the amount of time that each machine runs before breaking down is exponentially distributed with a mean of 3 days, and the amount of time required to fix a broken machine is exponentially distributed with a mean 2.4 days. On any given day, what is the expected number of machines that are running?

Solution

Machine running --- exp with mean 3 days

repair -- exp with mean 2.4

x =

E(no of machines that are running) = E(x) =3-2.4 = 0.6