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Math Help - Markov chain/transition matrix problem.

  1. #1
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    Markov chain/transition matrix problem.

    Hey, I am currently learning about markov chains in my data management course, and I am stuck on a problem.

    Question:
    Three people - John, Joan and Kim - throw a ball to each other. There is a probability of  \frac{1}{3} that John will throw the ball to Joan.
    There is a probability of  \frac {1}{2} that Joan will throw the ball to Kim.
    There is a probability of  \frac {1}{4} that Kim will throw the ball to John.
    a) Express this Markov chain as a transition matrix.

    Solution:
    Basically I am confused as to where to find the other probabilities. This is my transition matrix so far:
    -----Joan-----Kim-----John
    John-- 1/3-----------------
    Joan-----------1/2---------
    Kim---------------------1/4
    (hopefully that turns out okay, I don't know how to do it using latex)
    I know that each row is going to equal 1, so if I could find another probability in each row, I could finish the matrix. However, I do not know how to find the other probabilities.

    Help, please!
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  2. #2
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    Opalg's Avatar
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    Quote Originally Posted by Kakariki View Post
    Hey, I am currently learning about markov chains in my data management course, and I am stuck on a problem.

    Question:
    Three people - John, Joan and Kim - throw a ball to each other. There is a probability of  \frac{1}{3} that John will throw the ball to Joan.
    There is a probability of  \frac {1}{2} that Joan will throw the ball to Kim.
    There is a probability of  \frac {1}{4} that Kim will throw the ball to John.
    a) Express this Markov chain as a transition matrix.

    Solution:
    Basically I am confused as to where to find the other probabilities. This is my transition matrix so far:
    -----Joan-----Kim-----John
    John-- 1/3-----------------
    Joan-----------1/2---------
    Kim---------------------1/4
    (hopefully that turns out okay, I don't know how to do it using latex)
    I know that each row is going to equal 1, so if I could find another probability in each row, I could finish the matrix. However, I do not know how to find the other probabilities.

    Help, please!
    Look at that statement in red: nobody throws the ball to themself! So that only leaves two possibilities for each thrower...
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  3. #3
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    Quote Originally Posted by Opalg View Post
    Look at that statement in red: nobody throws the ball to themself! So that only leaves two possibilities for each thrower...
    Wow, I completely overlooked that fact! Thank you!!!!!!!!!!!
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  4. #4
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    Quote Originally Posted by Kakariki View Post
    Wow, I completely overlooked that fact! Thank you!!!!!!!!!!!
    I'm doing this course as well. I don't understand how to solve this question. How did your answer turn out ? ? ?
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