so im currently looking at Markov diagrams and stochastic matrices and have become quite stuck on some parts of this question below and was looking for some help.
Here is what I have done so far,
For (a) I have constructed a Markov diagram from given information that I have excluded from this question as its not entirely relevant as it just explains the rules of a game. And have proven that the associate matrix does indeed replicate the same as shown.
For (b) I have used the fact that the matrix is stochastic and used the left eigenvector of $\large[ 1 1 1 1 1 1 \large]$ to show that indeed $\lambda = 1$.
For (c)I have used the same eigenvector as in the last part and created the equations:
$1/2E+1/3C=M$
$1/2M+1/3S=E$
$1/2M+1/3S+1/2W=C$
$1/2E+1/3C+1/2N=S$
$1/3C+1/2N=W$
$1/3S+1/2W=N$
and $M+E+C+S+W+N=1$
But im not entirely sure how to use these equations to find the stable distribution.
And for (d) Im not entirely sure what to do here at all as this course has never involved the use of computors and hence I dont know what software to use to prove or disprove this.
Any help would be greately appreciated!