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Thread: Markov chain

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

    Consider a Markov Chain $\displaystyle X_0, X_1,...,$ with state space {1,2,3}, initial distribution $\displaystyle \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) $\displaystyle \mathbb{P} (X_2 | X_0 = 1)$
    (2) $\displaystyle \mathbb{P}(X_2 = 3)$
    (3) $\displaystyle \mathbb{E}(X_3)$
    (4) $\displaystyle \mathbb{P}(X_0=1 | X_3 = 3)$
    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 $\displaystyle X_0, X_1,...,$ with state space {1,2,3}, initial distribution $\displaystyle \pi^{0} = (1/3,1/3,1/3) $ and one-step transition matrix P where P is the attached image.

    Show

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

    $\displaystyle [1,0,0]P^2$

    For the second consider:

    $\displaystyle \pi_0 P^2$

    CB
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