Chapter 2 CT4 Q11 (iii)

[Peter Cook]

To find the stationary distribution we want to find values of pi_0, pi_1 & pi_2 in pi. Which satisfies pi=pi*P.

Where P =
0 0 1
0 1-p p
1-p p 0
In the solution to this question the matrix equations are as follows:
(1) pi_0 = (1-p)*pi_2
(2) pi_1 = (1-p)*pi_1 + p*pi_2
(3) pi_2 = pi_0 + p*pi_1

But when doing the vector-matrix multiplication the result comes out as:
(1) pi_0 = pi_2
(2) pi_1 = (1-p)*pi_1 + p*pi_2
(3) pi_2 = (1-p)*pi_0 + p*pi_1


I feel like I'm missing something, please can you help show where this result comes from?

 

[Peter Cook]

Sorry should have stated which year, this is from the September 2011 paper

 

[Andrew Martin]

Hi Peter

I think you may be using the rows instead of the columns of P in the matrix multiplication.

When we have <row vector> * <matrix>, the result is going to be another row vector where the first element is given by the dot product of <row vector> and the first column of <matrix>. The second element will be the dot product of <row vector> and the second column of <matrix> and so on.

Hope this helps!

Andy