Using this information, model Smalltown's weather as a Markov chain. $(30$ pts$)$

$(30$ pts$)$ Consider an inventory model in which the replenishment of stock takes place at the end of periods labelled $n=0,1,2,$dots, and we assume that the total demand for the single commodity during period $n$ is a random variable $Dn,$ independent of the time period. Assume that $P\{Dn=0\}=\mathrm{.}1,P\{Dn=1\}=\mathrm{.}2,P\{Dn=2\}=\mathrm{.}7.$ Assume that an $(S,s)$ policy is used: If the end$-$of$-$period stock is less than or equal to $s,$ then an amount sufficient to increase the quantity of stock on hand up to the level $S$ is immediately ordered; otherwise, no new stock is ordered. Assume that $S=2,s=-1.$ Let $x_n$ denote the quantity on hand at the end of period $n,$ just before restocking. A negative value of $x_n$ is interpreted as an unfilled demand that will be satisfied immediately upon restocking. This is the inventory example we studied in class; recall that $\{x_n,n0\}$ is a Markov chain. Draw one$-$step transition matrix. $(30$ pts$)$

Consider the mood of an individual is considered as a three$-$state Markov chain having a transition probability matrix.