Optimization and Simulation. Markov Chain Monte Carlo. Part 2

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Metropolis-Hastings algorithms: the main idea.
Lecture for the PhD course "Optimization and Simulation", EPFL.
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Hi Sir, thank you for all your fantastic videos.

How do you solve the system of equation at 6:39 to get the vector of probabilities to be in (perfect condition, partially damaged, seriously damaged, completely useless) = (5/8, 1/4, 3/32, 1/32) ?

Thank you very much

jossec