Mr. Smith works on a temporary basis. The mean length of each job he gets is three months. If the amount of time he spends between jobs is exponentially distributed with mean 2, then at what rate does Mr. Smith get new jobs?

Mr Smith gets a new job, every 5 months on the average.

Step-by-step explanation:

Mr Smith spends an average of 3 months on every job he gets.

Then he spends an average of 2 months in between jobs.

Meaning, on the average, if he has a job, he does it for 3 months, then leaves, lends the next 2 months without a job, then gets another job at the end of the 2 months without a job and then he repeats the cycle of 3 months on the job, 2 months without the job.

So, on the average it takes Mr. Smith, (3+2) months to get a new job.