# Thread: Need Urgent help for Markov Process!!

1. ## 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.

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