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Math Help - Need Urgent help for Markov Process!!

  1. #1
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    Question Need Urgent help for Markov Process!!

    I need help with this troubling question....please~~~
    Suppose there are 3 candidates, X,Y, n' Z, for the mayoralty of a town. Each week during the election campaign, candidate X loses 10% of their support to candidate Y, n' keeps the rest. Similarly each week candidate Y loses 30% of their support to candidate Z, n' keeps the rest. Similarly each week candidate Z loses 20% of their support to candidate X, n' keeps the rest. Initially support for candidates X,Y, n' Z is in the ratio of 20:20:60.
    (q) Explain why this situation meets the requirements for a Markov process n' find the transition matrix A, as well as the initial state vector v0 for this Markov process.
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  2. #2
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    Hello, skelly83!

    Suppose there are 3 candidates {X, Y, Z} for the mayoralty of a town.

    Each week during the election campaign:
    . . candidate X loses 10% of hisr support to candidate Y,
    . . candidate Y loses 30% of his support to candidate Z,
    . . candidate Z loses 20% of his support to candidate X

    Initially, support for candidates X, Y, Z is in the ratio of 20:20:60.

    Explain why this situation meets the requirements for a Markov process.
    Find (a) the transition matrix A, and (b) vector v_o for this Markov process.
    Let's baby=step through this problem . . .

    In one week, the following three things happen simultaneously:

    Candidate X loses 10% to Y. .He has 0.90X left.
    He also gains 20% of Z: . +0.2Z
    Hence, X becomes: . 0.9X + 0.2Z

    Candidate Y loses 30% to Z; he has 0.7Y left.
    He also gains 10% of X: . +0.1X
    Hence, Y becomes: . 0.7Y + 0.1X

    Candidate Z loses 20% to X; he has 0.8Z left.
    He also gains 30% of Y: . + 0.3Y
    Hence, Z becomes: . 0.8Z + 0.3Y


    (a) To transform (X,\,Y,\,Z) .to . (0.9X + 0.2Z,\:0.1X + 0.7Y,\:0.3Y + 0.8Z)

    . . the transition matrix is: . \boxed{A \;=\;\begin{pmatrix}0.9 & 0.1 & 0 \\ 0 & 0.7 & 0.3 \\ 0.2 & 0 & 0.8\end{pmatrix}}


    (b) . \boxed{v_o \:=\:(20,\,20,\,60)}

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