A simplified weather model has two states

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Error, Chance and the Machine, Ch Random walks and Markov chains

Problem

A simplified weather model has two states, sunny (S) and rainy (R), observed once a day. The transition matrix, with rows in the order (S, R), is P=(0.90.10.50.5).\mathsf{P} = \begin{pmatrix} 0.9 & 0.1 \\ 0.5 & 0.5 \end{pmatrix}. Find the stationary distribution π=(πS,πR)\boldsymbol\pi = (\pi_S,\pi_R).

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