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Math Help - BASIC Markov Process

  1. #1
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    BASIC Markov Process

    Just checking I got the process right- very simple Markov.

    If it is sunny on a particular day, it will definitely be rainy the next day. If it is rainy on a particular day, a flip of a coin will decide the weather for the next day (ridiculous, I know...).

    a.) What is the transition matrix that models this scenario?
    b.) If it is rainy on Tuesday, what is the probability that it will also be rainy on the following Friday?
    c.) In the long run, what is the percentage of days that it will be rainy?

    Thanks!
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  2. #2
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    Re: BASIC Markov Process

    Quote Originally Posted by jnow2 View Post
    Just checking I got the process right- very simple Markov.

    If it is sunny on a particular day, it will definitely be rainy the next day. If it is rainy on a particular day, a flip of a coin will decide the weather for the next day (ridiculous, I know...).

    a.) What is the transition matrix that models this scenario?
    b.) If it is rainy on Tuesday, what is the probability that it will also be rainy on the following Friday?
    c.) In the long run, what is the percentage of days that it will be rainy?

    Thanks!
    If you're checking your process, then you will have solutions and answers (otherwise you have nothing to check!). If you post all your working and answers, they can be reviewed for accuracy.
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  3. #3
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    Re: BASIC Markov Process

    Quote Originally Posted by mr fantastic View Post
    If you're checking your process, then you will have solutions and answers (otherwise you have nothing to check!). If you post all your working and answers, they can be reviewed for accuracy.
    I had written the transition matrix as:

    [0 0.5
    1 0.5]

    with a stationary vector of:
    [1
    0]

    Is that correct? or is the stationary vector using the coin toss scenario... e.g

    [0.5
    0.5]

    Using the original matrix, I deducted that x3 (the friday) =
    0.25
    0.75 and therefore, a 75% chance of studying on the friday?
    I'm not entirely sure how to complete the last section. Is it finding Xn?
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