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Math Help - Markov Chain Question

  1. #1
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    Markov Chain Questionc[Closed]

    To toss of a fair coin until 3 heads occur in a row.
    The transition matrix is
    \left(\begin{array}{cccc}0.5&0.5&0&0\\0.5&0&0.5&0\  \0.5&0&0&0.5\\0&0&0&1\end{array}\right)

    Question1 : Why are the elements on first column, row 2 and 3, are not zeroes?
    Will the following reasoning be correct?
    I am thinking: if the state space is
    { a_{o},a_{1},a_{2},a_{3}}, the first column must be
    must be reserved for probability of the nth toss being a tail.
    When the next toss is a Head, it proceeds to the next state; otherwise, it's back to column one.
    -----
    I posted this question on Sept 30, and I found my reasoning to be correct.

    Case closed.
    Last edited by novice; October 23rd 2009 at 12:44 PM. Reason: Case closed
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