A store that stocks a certain commodity uses the following (s, S) ordering policy. If its supply at the beginning of a time period is x, then it orders o(x) = 0 if x s, S x if x < s. The order quantity is immediately filled. The daily demands are independent and equal to j with probability j for j = 0, 1, 2, .... All demands that cannot be immediately met are lost. Let Xn denote the inventory level at the end of the nth time period. Argue that {Xn, n 1} is a Markov chain and compute its transition probabilities.