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Probability

Long-run share of rainy days

markov-chainstationary-distribution

Each day the weather is sunny, cloudy, or rainy, and tomorrow depends only on today:

  • From sunny: to sunny 0.50.5, to cloudy 0.30.3, to rainy 0.20.2.
  • From cloudy: to sunny 0.40.4, to cloudy 0.40.4, to rainy 0.20.2.
  • From rainy: to sunny 0.30.3, to cloudy 0.30.3, to rainy 0.40.4.

In the long run, what fraction of days are rainy?

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