1. Problem 15.4 Every day, it is either sunny or rainy on Rainbow Island. The weather for the next day depends only on today’s weather and yesterday’s weather. If the last two days were sunny, it will be sunny on the next day with probability 0.9. This probability is 0.45 if the last two days were rainy.

The next day will be sunny with probability 0.7 if today’s weather is sunny and yesterday’s weather was rainy. If today’s weather is rainy and yesterday’s weather was sunny, it will be sunny on the next day with probability 0.5. Define a Markov chain describing the weather on Rainbow Island and specify its one step transition probabilities.

15.1 Markov model 393