Hi, can someone help me with this multiple choice. Thank you

(a) In = 0.5 and 1r] = 0.5 are the stadyrstate probabilities for the follow, (e) Let ing Markov chain: 11 11 1/2 1/2 1 P: 1 1/3 1/3 1/3 2 1/4 3/4 0 in the long run. the fraction of time that the system is in state 1 is: i. 412 11. % iii. 4; i. This statement is True ' ii. This statement is False (l') 110'. 1) 0 1/2 1/2 (1 (ii) If there exist at least one state 1' that 17,-,- > t) for an irreducible [inite- 1 1/4 1/2 t) 1/4 state Markov chain, then the Markov chain is aperiodic. P = 2 0 (l 1 (l i. This statement is True 3 1) (I 0 1 il' This statement is False the probability that in the long r1111 the system is in state 3 given that today the (c) [11 general, if state'i is reachable from state 1', then state 31' is reachable system is in state I) is: from state 1'. . 2 l. 5. i. This statement is True ii 1 . 3. ii. This statement is False 1 111. Z' (d) For the following MNkDV Chain, Pixu = 1.XIJ = 1) = 1- iv. Cannot be estimated. i. This statement is 'Ii'ue i. This statement is False