Consider a Markov chain with the states {1, 2, 3, 4, 5} and the TPM below. Please list the classes and state whether they are recurrent, transient, or absorbing. Calculate the period for each class and state whether or not it is ergodic. Finally, classify the Markov chain as irreducible ergodic, ergodic, or not ergodic. 0.4 0.1 0.5 0 DOOO DOHO P = 0 1 0.3 0.5 0.2 0.1 0 0.2 0.3 0.4