Hi, can you help me with this problem, please?
I have tried but I am not sure what to do exactly...
Yn - sum of n independent rolls of a fair die.
Find lim P{Yn is a multiple of 13), n->inf
How can I define the appropriat Markov chain?
I know that after defining it I can use the limiting probability
If you can help me with this will be greatly appreciated.
Thank you!
The point is that if you throw a single dice you may assume that each of the faces comes up with probability 1/6 and the faces show the values 1,2,3,4,5,6.
From that you can work out the transition matrix.
So if , then:
with prob ,
with prob ,
with prob ,
with prob ,
with prob ,
with prob .
CB
So, I have got for the transition matrix
A=[0 1/6 1/6 1/6 1/6 1/6 1/6 0 0 0 0 0 0;
0 0 1/6 1/6 1/6 1/6 1/6 1/6 0 0 0 0 0;
0 0 0 1/6 1/6 1/6 1/6 1/6 1/6 0 0 0 0;
0 0 0 0 1/6 1/6 1/6 1/6 1/6 1/6 0 0 0;
0 0 0 0 0 1/6 1/6 1/6 1/6 1/6 1/6 0 0;
0 0 0 0 0 0 1/6 1/6 1/6 1/6 1/6 1/6 0;
0 0 0 0 0 0 0 1/6 1/6 1/6 1/6 1/6 1/6;
1/6 0 0 0 0 0 0 0 1/6 1/6 1/6 1/6 1/6;
1/6 1/6 0 0 0 0 0 0 0 1/6 1/6 1/6 1/6;
1/6 1/6 1/6 0 0 0 0 0 0 0 1/6 1/6 1/6;
1/6 1/6 1/6 1/6 0 0 0 0 0 0 0 1/6 1/6;
1/6 1/6 1/6 1/6 1/6 0 0 0 0 0 0 0 1/6;
1/6 1/6 1/6 1/6 1/6 1/6 0 0 0 0 0 0 0]
and for the limit I raised it A^30 and got 0.0769
Is that correct?
Thank you so much!