Q4: Suppose we apply the Markov model on the transition matrix of the web where

Question

Q4: Suppose we apply the Markov model on the transition matrix of the web where the transition matrix MT-B is 1 0 2 3 2 1 0 0 A hypothetical example of a Web Find the probability of being at state i, i=1,2,3,4 at infinity (or steady state). i) You can use the iteration Pk+1 B Pk with initial state probabilities Po= [0.25 0.25 0.25 0.25] T to calculate the steady state probability values. ii) or, you can solve the equation: P= BP You should get the same answer in parts (i) and (ii). You can use MATLAB

Explanation / Answer

MATLAB code

close all
clear
clc

B = [0 1/2 1 0;
     1/3 0 0 1/2;
     1/3 0 0 1/2;
     1/3 1/2 0 0]';
P = [0.25 0.25 0.25 0.25]';

% part (i)
fprintf('Part (i) ');
while 1
    P_prev = P;
    P = B*P;
    c = 0;
    for i=1:length(P)
        if abs(P(i) - P_prev(i)) <= 1e-6
            c = c + 1;
        end
    end
    if c == length(P)
        break
    end
end
Pinf = P

% part (ii)
fprintf(' Part (ii) ');
P = [0.25 0.25 0.25 0.25]';
Pinf = pinv(B)*P

Output

Part (i)
Pinf =
    0.2500
    0.2500
    0.2500
    0.2500

Part (ii)
Pinf =
    0.2500
    0.2500
    0.2500
    0.2500

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