Consider a simple stochastic model of the weather in Syracuse in which each day is classified as either Sunny, Rainy or Windy. T
he weather tomorrow ONLY depends on the weather today, but NOT on the weather of previous days. If today is Sunny, then tomorrow is Sunny with probability 40%; tomorrow is Windy with probability 60%.
If today is Rainy, then tomorrow is Sunny with probability 25%; tomorrow is Rainy with probability 50%.
If today is Windy, then tomorrow is Sunny with probability 33%; tomorrow is Windy with probability 33%.
a. Find the transition matrix P describing the model.
b. If today is Sunny what is the probability that it will be Rainy after 3 days?
