In the town, the weather pattern has three categories each day:Windy, Rainy or Sunny. The weather pattern each day follows aMarkov chain model. If it is windy on a day, the following day willbe sunny for sure; if it is rainy, the following day will be rainywith probability 0.25 otherwise sunny; and if it is sunny, thefollowing day will be windy with probability 0.25, Rainy withprobability 0.25 and sunny otherwise. A worker is paid $175, $125and $75 on days work depending on if it is Windy, Rainy or Sunny,respectively.
a. Write the transition matrix for this weather pattern
b. How much does the worker get paid on an average day?
