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Math Help - Markov Chain Limiting Probabilities (Just need answer checked please)

  1. #1
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    Markov Chain Limiting Probabilities (Just need answer checked please)

    Three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck . What fraction of vehicles on the road are trucks?

    Let

    state 0 represent seeing a truck
    state 1 represent seeing a car

    Then we have a probability matrix of



    \pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})

    0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}

    I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks
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  2. #2
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    Re: Markov Chain Limiting Probabilities (Just need answer checked please)

    Quote Originally Posted by downthesun01 View Post
    Three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck . What fraction of vehicles on the road are trucks?

    Let

    state 0 represent seeing a truck
    state 1 represent seeing a car

    Then we have a probability matrix of



    \pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})

    0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}

    I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks
    Up until the very last step, the answer is 0.2/0.95=20/95 ~= 0.2105

    CB
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    Re: Markov Chain Limiting Probabilities (Just need answer checked please)

    Thank you very much
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