I have a doubt in this question.

Question

It is well known to the Public Health Service that Harry’s Restaurant gives

only casual attention to matters of cleanliness; consequently, the Public

Health Service periodically closes the restaurant and mandates a cleanup.

Independent periods of operation and closure form two independent renewal processes.

The open periods are iid with means μ0, and the closed

periods are iid with means μ1. Lengths of open periods and closed periods

are independent of each other. Answer the following questions :

(a) What is the long-run proportion of time that Happy

Harry’s Restaurant is open to its adoring public.

(b) In the long run, what is the average number of times the

restaurant remained open.

Answer 1

Hi Vikram K.,

Looks like your doubt might relate to the odd language ("renewal processes")? Proportion open = μ0/(μ0+μ1) (from consideration of one cycle); then number of times open = t / (μ0+μ1) since one time open requires an interval open plus an interval shut!

P.S. Unless proportion open is very high, I would eat elsewhere or prepare your own meals -- I wondered where all those road kills were disappearing to ...

-- Cheers, -- Mr. d.