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July 7th, 2014, 07:32 AM   #1
Joined: Jun 2014
From: SriLanka

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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..
Hemantha is offline  
July 7th, 2014, 12:57 PM   #2
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{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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