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Homework Help: Intro to Markov Chains

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data
    On any given day, Amy is either cheerful (C), neutral (N), or mad (M). If she is cheerful today, then she will be C, N, or M tomorrow with probabilities 0.5, 0.4, 0.1 respectively. The rest of the probabilities are given so that we can get the probability matrix P:

    P = [
    0.5 0.4 0.1
    0.3 0.4 0.3
    0.2 0.3 0.5
    ]

    Amy is currently in a cheerful mood. What is the probability that she is not in a mad mood on any of the following three days?

    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure how to go about this. To find the probability that Amy would be mad in 3 days, I would find P3 and look at the (1,3) entry, correct?

    Then to find the probability that she is NOT mad in 3 days, I'd take 1 minus that probability.

    But it doesn't ask for the 3rd day, it asks for "any of the following 3 days". I'm confused about how to do that!

    The solutions manual changes the matrix to
    [
    0.5 0.4 0.1
    0.3 0.4 0.3
    0.0 0.0 1.0
    ]

    Raises that to the power of 3, then takes 1 - [the (1,3) entry of the matrix]

    I don't get why. Thanks!
     
  2. jcsd
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