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July 7th, 2014, 07:32 AM  #1 
Newbie Joined: Jun 2014 From: SriLanka Posts: 5 Thanks: 0  Do you know Markov chain?
A particle moves on a circle through points which have been marked 0, 1, 2, 3, 4 (in a clockwise order). At each step it has a probability p of moving to right (clockwise) and (1p) to the left (counterclock wise). Let X n denote its location on the circle after the nth step. (i) Explain why {X n , n ≥ 0} is a Markov chain. (ii) Find the transition probability matrix. Please Help me.. 
July 7th, 2014, 12:57 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,443 Thanks: 564 
{i} Essentially by definition. The distribution of X(n+1) depends entirely on the value of X(n). (ii) (I forgot the exact form of a transition matrix). Each row should look like (1p),0,p,0,0 rotated. First row p in second column, second row p in third column, etc. (I may have rows and columns interchanged). 

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