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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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