In each of the graphs pictured, assume that each arrow leaving a vertex has an equal chance of being followed. Hence if there are thee arrows leaving a vertex then there is a 1/3 chance of each being followed.
- For each of the six pictures, find the Markov transition matrix.
- State if the Markov chain given by this matrix is irreducible and if the matrix is doubly stochastic.
- If the Matrix is irreducible, state if it is aperiodic.
- When possible (given what you know), state if each chain has a unique stationary distribution. If it is obvious that the system does not possess a unique stationary distribution, please state why.
- For two of the chains it is easy to state what is this unique stationary distribution . Which two and what are the two stationary distributions?