Powers of the transition matrix and state vectors Problem set A Answers

1. (a) 0.568
2. (b) 0.610

0.336

1. (a) 0.413
2. (b) 0.238

\(\begin{pmatrix} 0.593 \\ 0.407 \end{pmatrix}\)

\(\begin{pmatrix} 0.272 \\ 0.359 \\ 0.369 \end{pmatrix}\)

1. (a) Regular. The smallest power is 2.
2. (b) Not regular. The first and third states are absorbing, so zeros stay in every power.
3. (c) Not regular. The chain goes round state 1, 2, 3, 1, … and \(\mathbf{T}^3\) is the identity matrix, so every power has zeros.

Atlas 32.9%, Bolt 42.9%, Core 24.3%

0.242

morning 873, evening 327

1. (a) 0.096
2. (b) 0.312

n = 7

1. (a) 0.2952
2. (b) \(\mathbf{T}^2\) entry in column A, row C is 0.2952