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February 2nd, 2015, 10:26 AM  #1 
Newbie Joined: Dec 2012 Posts: 27 Thanks: 0  Markov Chains
Hi , I am trying to classify the subsets of this Markov chain I am unsure if one of the subsets is {2, 3, 4} or it is {2, 4}. So 2 and 4 obviously communicate but I have not seen an example where another number joins two communicating classes in this way (i.e. 3). Could someone help me clear this up please? 
February 2nd, 2015, 12:18 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 669 
You need to explain the diagram.

February 2nd, 2015, 02:50 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, interestedinmaths! Quote:
You seem to have this matrix: $\quad \begin{pmatrix}0&1&0&0&0&0 \\ 0&0&\frac{1}{2}&\frac{1}{2}&0&0 \\ 0&0&0&1&0&0\\ 0&1&0&0&0&0 \\ 0 & \frac{1}{3} &0& \frac{1}{3} &0& \frac{1}{3} \\ \frac{1}{2} &0&0&0&\frac{1}{2}&0 \end{pmatrix}$ What exactly is the question?  
February 2nd, 2015, 07:05 PM  #4  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2603 Math Focus: Mainly analysis and algebra 
I suspect that this is the sort of thing we are after Quote:
Subsidiary definitions: Quote:
 
February 3rd, 2015, 01:05 AM  #5 
Newbie Joined: Dec 2012 Posts: 27 Thanks: 0 
Thanks for all the replies. Apologies for not being more descriptive. I have the matrix that soroban mentions and I wanted to draw the corresponding Markov chain. When drawing it, I was not sure how to identify the communicating classes. I was stuck deciding whether it was {2,4} and {5,6} or {2, 3, 4} and {5, 6}. So could it be said as 4 communicates to 2, and 2 communicates to 3, 3 to 4, and 4 back to 2 they all communicate with each other? 
February 3rd, 2015, 03:29 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2603 Math Focus: Mainly analysis and algebra 
Yes. 2 and 4 are not a communicating class because from 4 you can get to 3 and back again. (The same goes for 2).


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