Observable Markov Model. Consider a simple 3-state Markov model of the weather. We assume that once a day (e.g. at noon), the weather is observed as being one of the following: State 1: rain or snow State 2: cloudy State 3: sunny We postulate that the weather on day t is characterized by a single one of the three states above. We have the following transition probabilities: a. Given that the weather on day 1 (t=1) is rainy, what is the probability that the weather on the next five days is: {S1, S2, S3, S3, S1}? b.Given that the model is in a known state, what is the probability it stays in that state for exactly d days? c. What is the expected number of observations in a state?

Note: d=1dad1=(a1)21