Consider a discrete time periodic inventory model and let e$,$ be the total demand in period n and let X$,$ be the inventory quantity on hand at the end of period n$.$ Assume that $($s$,5)$ inventory policy is used. That is$,$ if the end of period stock is not greater than s$,$ then a quantity is immediately procured to bring the level up to S$.$ If the end of period stock exceeds s$,$ then no replenishment takes place. Suppose that s$=2$ and S$=4$ and $81,$ Ez$,.,$ En are independent random variables where P$(=0)=0\mathrm{.}1,$ P$($a $=1)=0\mathrm{.}4$ and P$($a $=2)=0\mathrm{.}5$ for i$=1,2,3,...,$n Then Xo$,$ Xi$,...,$ X$.$ is a Markov Chain. First define