3. Consider the Markov chain defined on states S - {0, 1, 2, 3} whose transition probability matrix is 1/2 1/2 0 0 P 1/4 3/4 O 1/4 1/4 1/4 1/4 0 0 0 1 (a) Find all communicating classes; which classes are transient and which are recurrent? Further classify any recurrent classes as positive or null recurrent. (b) In words, describe the long-term behavior of this Markov chain. (Hint: Does a stationary distribution exist? Why or why not? Does it matter in which state the chain starts?)