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Math Help - Hitting probabilities

  1. #1
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    Hitting probabilities

    Please help on hitting probabilities, I can't remember how to do this basic stuff.

    Markov chain have states 1-4 has one-step transition matrix
    \left(\begin{array}{ccccc}\frac{1}{8}&\frac{1}{8}&  \frac{1}{8}&\frac{1}{8}&\frac{1}{8}\\0&\frac{3}{4}  &0&0&\frac{1}{4}\\0&0&\frac{1}{2}&0&0\\\frac{1}{2}  &0&0&0&0\\0&\frac{1}{2}&0&0&\frac{1}{2}\end{array}  \right)
    For each state i, find

    a_i = P(process ever reaches K = {2,5}  | X_0 = i)

    Thank you
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    That is the probability of going from state two to state five. It is in row two and column five. Matrices are always listed (r, c) for row and column. The probability is one in four.
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  3. #3
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    Thank you, just one more question.

    So no matter how big the square matrix is, I just need to look at the row two and column five for that question?
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