2. Consider a Markov chain with state space S = 0, 1, 2, 3, 4, 5 with the
transition matrix
$\begin{bmatrix}
0 & 0 & 2/5 & 3/5 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1/2 & 1/2 \\
0 & 0 & 0 & 0 & 2/3 & 1/3 \\
1/2 & 1/2 & 0 & 0 & 0 & 0 \\
1/4 & 3/4 & 0 & 0 & 0 & 0
\end{bmatrix}$
a) Draw the digraph for the MC.
b) Clearly label the states as completely as possible. Credits will be given for
correct extra effort.
c) Compute $P^n$, n = 2, 3, 4, 5, 6. Any comment?