Consider a Markov chain {X, : n = 0, 1, - .-} on the state space S = {1,2,3,4} with the following transition matrix: 1/3 2/3 1/2 1/2 P = 1/4 3/4 1/4 1/4 1/2 Find Pr(X7 = 2|X1 = 3). %3D Determine the class(es) of the above Markov chain. Specify which state is recurrent and which state is transient. Justify your results.

Q4) A Markov source as given in the table below: si S2 S3 P(S1)=0.2 P(S2)=0.2 P(S3)=0.6 PI2=0.3 P21=0.3 P31=0.35 P13=0.4 P22=0.7 P32=0.3 Draw Markov diagram then Calculate 1) Average source Entropy? 3) Prove that: G,>G;

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A Markov chain {s} with state space n={1, 2, 3} has a sequence of realizations and process transitions as follows: Transition (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3.1) (3,2) (3,3) t S: S+1 2 1 1. 1 1 1 1 1 3 1 3 3 3 4 3 1. 2 3 1. 2 1 7 2 2 1. 8 2 2 1 9 2 3 1. 10 3 11 1 1 12 1 1. 13 1 1. 14 1. 1. 15 3 1. 1. 16 1. Number of frequencies : 1 3. 2 2 1 1 1 1 a. determine the transition frequency matrix O= 2 12 93 021 022 °23 %3D 31 °32 °33) 1 P1 P12 P13 b. determine the estimated transition probability matrixP= 2 P21 P22 P23 3 P31 P32 P33)