Please help me with 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. Thank you.

(Please consider a' = 0 and b' = 1)

3. Let {Xx : k 2 1} denote a random sequence taking values in {1, 2, 3} which forms a Markov chain. Let a' = 0 and b' = 1 . For this Markov chain, we have the transition probabilities P(Xn+1 = 2|Xn = 1) = 5 + a' , P(Xn+1 = 3\\Xn = 1) = 4- a' 16 16 2- b' P(Xn+1 = 1/Xn = 2) = 8 , P(Xn+1 = 3[Xn = 2) = 4 - P(Xn+1 = 1\\Xn =3) =0 , P(Xn+1 = 2|Xn = 3) = 8 (a) Compute the remaining entries in the transition matrix and write out the matrix. (b) Draw a diagram of the chain and obtain the steady state distribution (#1, /2, M3) of this Markov chain. (c) The entropy rate of the chain in steady state is given by Co [ MR. H(Xn+1 | Xn = k). k=1 Obtain the entropy rate