Weather simulation using stochastic modeling
Question
In a particular area, there are 2 types of weather: sunny and rainy. The following is observed across a couple year period.
- Assuming it's sunny, the probability of the weather staying sunny the following day is 80%
- Assuming it's sunny, the probability the weather will change from sunny to rainy is 20%
- Assuming it's rainy, the probability the weather staying rainy the following day is 70%
- Assuming it's rainy, the probability the weather will change from rainy to sunny is 30%
Given this information, create a transition matrix and run a simulation of the weather over a 1000 day period. Next, using your simulation results, estimate the stationary distribution.
If you need a refresher, here is a resource on Markov Chains.