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Math Help - Markov chain

  1. #1
    Junior Member BrooketheChook's Avatar
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    Markov chain

    Consider a Markov Chain X_0, X_1,..., with state space {1,2,3}, initial distribution \pi^{0} = (1/3,1/3,1/3) and one-step transition matrix P where P is the attached image.

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    (1) \mathbb{P} (X_2 | X_0 = 1)
    (2) \mathbb{P}(X_2 = 3)
    (3) \mathbb{E}(X_3)
    (4) \mathbb{P}(X_0=1 | X_3 = 3)
    Attached Thumbnails Attached Thumbnails Markov chain-transition-matrix.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by BrooketheChook View Post
    Consider a Markov Chain X_0, X_1,..., with state space {1,2,3}, initial distribution \pi^{0} = (1/3,1/3,1/3) and one-step transition matrix P where P is the attached image.

    Show

    (1) \mathbb{P} (X_2 | X_0 = 1)
    (2) \mathbb{P}(X_2 = 3)
    (3) \mathbb{E}(X_3)
    (4) \mathbb{P}(X_0=1 | X_3 = 3)
    For the first consider:

    [1,0,0]P^2

    For the second consider:

    \pi_0 P^2

    CB
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