A supplier of toner cartridges of a certain brand checks her stock every Monday. If the stock is less than or equal to \(s\) cartridges, she orders an amount of \(S-s\) cartridges, which will be available the following Monday, \(0 \leq s

\[p_{i}=P(D=i) ; \quad i=0,1, \ldots\]

Let \(X_{n}\) be the number of cartridges on stock on the \(n\)th Sunday (no business over weekends) given that the supplier starts her business on a Monday.

(1) Is \(\left\{X_{1}, X_{2}, \ldots\right\}\) a Markov chain?

(2) If yes, determine its transition probabilities.