9. A bookstore keeps daily track of the inventory level of a popular book to restock it to a level of 100 copies at the start of each day. The data for the last 30 days provide the following end-of-day inventory position: 1,2,0,3,2, 1,0,0,3,0, 1,1, 3,2,3,3,2,1,0,2,0,1,3, 0,0,3,2, 1,2,2.

(a) Represent the daily inventory as a Markov chain.

(b) Determine the steady-state probability that the bookstore will run out of books in anyone day.

(c) Determine the expected daily inventory.

(d) Determine the average number of days between successive zero inventories.