Basic Markov Chain I




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.

  1. For each of the six pictures,  find the Markov transition matrix.
  2. State if the Markov chain given by this matrix is irreducible.
  3. If the Matrix is irreducible, state if it is aperiodic.

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