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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 (clock-wise) and (1-p) to the left (counter-clock 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: 6,807 Thanks: 717 {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 (1-p),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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# a particle moves on a circle through points that have been marked 0 1 2 3 4

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