Transition Probabilities

$1$ point possible $($graded$)$

Refer to the MDP described and depicted in the $33$ grid on the top of this page.

Assume that the transition probabilities for all the states are given as a table $M,$ whose $(i,j,k)-$th entry is

$M[i][j][k]=T(s_i,a_j,s_k)=P(s_k|s_i,a_j),$ which represents the transition probability of ending up at

state $s_k$ when action $a_j$ is taken from the state $s_i.$ Note: Note that here, $s_i$ and $s_k$ can be any pair of states,

not necessarily reachable by an action in one step.

Enter the number of entries in the table $M$ :