Lectures - 8.3 Regular Markov Chains

The cafeteria at Peter's school serves pizza and hot dogs on Tuesday. Let state 1 be having pizza and state 2 be having hot dog. He is four times as likely to have hot dog as pizza this week. Find the initial state vector.

Peter's transition matrix:

He is four times as likely to have hot dog as pizza this week. What's the probability that he'll eat pizza 3 weeks from now?

Determine if the following is regular.

Peter's transition matrix:

Find his long run stable vector W.