Question

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?

Answer 1

11/14

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