Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 1. If every state of a Markov chain is an absorbing state, then it is an absorbing...

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.

1. If every state of a Markov chain is an absorbing state, then it is an absorbing chain.

2. If a Markov chain is absorbing, then it has a unique stationary matrix.

3. If a Markov chain is absorbing, then it is regular.

4. If a Markov chain is regular, then it is absorbing.