I need questions a,b, and c. Really appreciate it if you can solve these with a proper explanation. So that I can understand how to do them. Can you please calculate the stationary distribution by using probability equation (?_1 + ?_2 = 1 ) in question (a) and (b).

Thank you.

4. Consider the Markov chains given below: (a) Let a 2state Markov chain on {1,2} be given by p(2 I 1) = 1/4, and p(l | 2) = 1 / 3. Draw a diagram for this Markov chain and nd its stationary distribution. (b) If the chain in part (a) is in state 11 how long (how many discrete time units) does it take it on average to transition to state 2? Justify your answer fully. (e) Let a 3state Markov chain on {1, 2, 3} be given by p(2|1) = 1/2, p(3|1)=1/4; p(3|2) = 1/3, p