A supplier of toner cartridges of a certain brand checks his stock every Monday. If the stock is less than or equal to s cartridges, he orders an amount of S – s cartridges, which will be available...

A supplier of toner cartridges of a certain brand checks his stock every Monday. If the stock is less than or equal to s cartridges, he orders an amount of S – s cartridges, which will be available the following Monday, 0 ≤ s <>

Let be the number of cartridges on stock on the X_n
nth Sunday (no business over weekends) given that the supplier starts his business on a Monday.

(1) Is {X₁, X₂, ...} a Markov chain?

(2) If yes, obtain the matrix of the transition probabilities.