Monica works on a temporary basis. The mean length of each job she gets is 11 months. If the amount of time she spends between jobs is exponential with mean 3 months, then in the long run what fraction of the time does she spend working?

11/14

Step-by-step explanation:

Since the job and jobless cycles of Monica will follow an alternating renewal process,

Let

Ji=duration of i-th job period

Li=duration of i-th jobless period

E (Ji) = 11 and E (Li) = 3

Hence,

The fraction of the time does she spend working in long run is given by the formula = E (Ji) / (E (Ji) + E (Li))

=11 / (11+3)

=11/14