A beer vendor adopts the following stock replenishment policy: every Monday morning he

buys fixed number N of six-packs of beer from the distributor, and sells the beer during the

week. No matter how many packs he sells during that week, next Monday morning he will

buy again N six-packs. Assume that the demand Dn for beer on week n is independent of the demand in previous weeks, and that its distribution is given by P(Dn=i) = di, i = 0, 1, 2, . . . (i is the number of six-packs).

Let Xn be the number of beer packs in the store at the end of the nth week.

Show that

{Xn} is Markov chain, and determine its state-space and transition matrix.