Problem 1 [50']For each of the following transition matrices, do the following: (1) Determine whether the Markov chain is irreducible; (2) Find a stationary distribution ; is the stationary distribution unique?; (3) Determine whether the Markov chain is periodic; (4) Give the period of each state. (5) Without using any software package, find plapproximately (a) 0 1/3 2/3 P = 2/3 0 1/3 1/3 2/3 0 (b) P = 4 00 0 MHOO