2.Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} withtransition matrix(1/2 1/2 0 01/7 0 3/7 3/71/3 1/3 1/3002/3 1/6 1/6/(a) Explain how you can tell this Markov chain has a limiting distribution and howyou could compute it.

Given that be the Markov chain on state space with transition matrix:

Answered: Let Xo, X₁,... be the Markov chain on…

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5. Let P be the transition matrix of a Markov chain with finite state space. Let I be the identity matrix, U the |S| x |S| matrix with all entries unity, and 1 the row |S|-vector with all entries unity. Let л be a non-negative vector with Σ; i = 1. Show that лP = if and only if (I-P+U) = 1. Deduce that if P is irreducible then = 1(I-P + U)-¹.
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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Find the limiting distribution for this Markov chain.
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)
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Let Xo, X₁,... be the Markov chain on state space {1, 2,3,4} with 2. transition matrix 1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.