Hello, skelly83!

Let's baby=step through this problem . . .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 , and (b) vector for this Markov process.

In one week, the following three things happen simultaneously:

Candidate X loses 10% to Y. .He has left.

He also gains 20% of Z: .

Hence, becomes: .

Candidate Y loses 30% to Z; he has left.

He also gains 10% of X: .

Hence, becomes: .

Candidate Z loses 20% to X; he has left.

He also gains 30% of Y: .

Hence, becomes: .

(a) To transform .to .

. . the transition matrix is: .

(b) .