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?
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
