MARKOV CHAINS: 1. Suppose that today's weather depends only on yesterday's weather. If it rained yesterday, the chances of rain today are 50 percent; if it did not rain yesterday, the cha...
MARKOV CHAINS: 1. Suppose that today's weather depends only on yesterday's weather. If it rained yesterday, the chances of rain today are 50 percent; if it did not rain yesterday, the chances of rain today are 20 percent. Answer the following questions: (a) Find the transition matrix of this process. (b) Find the 2-step transition matrix. (c) If it rained on Monday, what is the probability it will also rain on Wednesday? FI (d) What is the long-term probability of a rainy day? 0.5Y
MARKOV CHAINS: 1. Suppose that today's weather depends only on yesterday's weather. If it rained yesterday, the chances of rain today are 50 percent; if it did not rain yesterday, the chances of rain today are 20 percent. Answer the following questions: (a) Find the transition matrix of this process. (b) Find the 2-step transition matrix. (c) If it rained on Monday, what is the probability it will also rain on Wednesday? FI (d) What is the long-term probability of a rainy day? 0.5Y