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**Code for:** Markov Chains

**Solution:**

```
%% Function
function [channel] = markovChain2States(P, lengthChain)
channel = zeros(1, lengthChain); % 2-state Markon chain (output vector)
channel(1) = randi([1 2],1,1); % step a)
for i = 2:lengthChain
event = randi([1 100],1,1)/100; % step b)
if channel(1,i-1) == 1 % step c)
if event <= P(1,1) % switch to state 2
channel(1,i) = 2;
else
channel(1,i) = 1;
end
elseif channel(1,i-1) == 2 % step d)
if event <= P(1,1) % switch to state 1
channel(1,i) = 1;
else
channel(1,i) = 2;
end
end
end
[V,D] = eig(P');
% Analytical eigenvalues
%diag(D)
ix = find(isAlways(diag(D) == 1,'Unknown','error'));
%diag(D(ix,ix))
% analytical stationary distributions. The eigen vectors are normalized with the 1-norm
for k = ix'
V(:,k) = simplify(V(:,k)/norm(V(:,k)),1);
end
%Probability = V(:,ix)
fsurf(Probability(1), [0 1 0 1]);
xlabel a
ylabel b
title('Probability of A');
figure(2);
fsurf(Probability(2), [0 1 0 1]);
xlabel a
ylabel b
title('Probability of B');
end
% in command line enter markovChain2States(2,5) or your desired input
% arguments.
```

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