Consider the Markov Decision Process $($MDP$)$ with transition probabilities and reward function as given in the tables below. Assume the discount factor y$=1($i$.$e$.,$ there is no actual discounting$).$ sa R$($sa$)$ a s$\text{'}$ T$($s$,$ a$,$ s$\text{'})$ A$1$A A$1$B $00\mathrm{.}50\mathrm{.}5|2$ T$($s$,$ a$,$s$\text{'})$ sa Rs$,$ a $20$ We follow the steps of the Policy Iteration algorithm as explained in the class. $1.$ Write down the Bellman equation. $2.$ The initial policy is $7($A$)=1$ and $7($B$)=1.$ That means that action $1$ is taken when in state A$,$ and the same action is taken when in state B as well. Calculate the values V$"($A$)$ and V$.($B$)$ from two iterations of policy evaluation $($Bellman equation$)$ after initializing both VT $($A$)$ and VT$($B$)$ to $0.3.$ Find an improved policy Tnew based on the calculated values VT $($A$)$ and V$($B$).$