Question

2. Suppose the weather in Saratoga Springs is either sunny, cloudy, or snowy on any there is a 60% chance that given winter day. If the weather is sunny today, it will be sunny tornorrow, a 30% chance that it will be cloudy tomorrow, and a 10% chance that it will be snowing. If it is cloudy today, there is a40% chance it will be sunny t will continue to just be tomorrow a 30% chance it will snow and a 30% chance that i Cloudy. Finally, if it is snowing today, there is a 10% chance that it will still be tomorrow and a 40% chance that it will be sunny. The forecast for today brninng 70% chance of clouds and 30% chance of sun (0% chance of snow). a. Write the stochastic matrix W describing the probability of weather types. Also write the initial vector v to describe the weather "today." b. Determine Wv c. What is the chance of snowy weather tomorrow? d. Consider an initial vector v 0.4 for Monday. Using this vector, determine 0.6 the probability of sunny weather on Wednesday e. Calculate the steady state vector q for W. In the long run, what is the probability that the weather will be sunny on any given winter day?

Answer 1

Maximum we can solve four sub parts

SU | 30 9 3o% 50 2 2 2 3 1 0.7 0.30 024 2

0 0.6 о +0.12 +0.06 0:10 0 1240 126 oo 0 336