please help me solve this question, thank you

A Markov chain {X, , n = 0,1,2,...} with state space S = {0, 1, 2,3} is applied to model a process. The transition probabilities between states in one year are given by: 0.7 0.3 0 0 0.2 0.8 0 0 P = (Pi; )4x4 = 0.1 0.3 0 0.6 0.4 0 0.6 0 (a) For this Markov chain, determine whether it is reducible or irreducible, and its states are periodic or aperiodic. [2] (b) Find all stationary distributions of this Markov chain. [3] (c) Determine whether lim P" and lim Pr (X, =i) exist or not and justify your answers. n -too n-too Find the limits that exist. [5] (d) At the end of each year, the process incurs a cost of 80 if it is in state 0 at the start of the year, 50 if in state 1, and 20 if in state 2 or 3. Given that the process is in state 0 at the start of the first year, calculate the expected present value of the total cost of the process over all future years (including the first year) at interest rate 5% pa. [5]