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

1. (a) 0.663
2. (b) 0.396

0.262

1. (a) 0.430
2. (b) 0.226

\(\begin{pmatrix} 0.537 \\ 0.463 \end{pmatrix}\)

\(\begin{pmatrix} 0.300 \\ 0.360 \\ 0.341 \end{pmatrix}\)

1. (a) Regular. The smallest power is 2.
2. (b) Not regular. The second state is absorbing, so zeros stay in column 2 of every power.
3. (c) Not regular. The chain swaps state 1 and state 2 every step and \(\mathbf{T}^2\) is the identity matrix, so every power has zeros.

Nova 27.9%, Orbit 46.9%, Pulse 25.2%

0.267

app 833, card 367

1. (a) 0.0743
2. (b) 0.606

n = 7

1. (a) 0.2412
2. (b) \(\mathbf{T}^2\) entry in column B, row A is 0.2412