Question 2 Winston 172 Problem 4 Smalltown weather depends o

Question 2. [Winston 17.2 Problem 4] Smalltown weather depends on the last two days of Smalltown weather, as follows: (1) If the last two days have been sunny, then 95% of the time, tomorrow will be sunny. (2) If yesterday was cloudy and today is sunny, then 70% of the time, tomorrow will be sunny. (3) If yesterday was sunny and today is cloudy, then 60% of the time, tomorrow will be cloudy. (4) If the last two days have been cloudy, then 80% of the time, tomorrow will be cloudy.

(a) Using this information, model Smalltowns weather as a Markov chain, i.e., draw the state transition diagram. (Hint: Markov chain transitions do not dependent on the previous states and a state does not necessarily consist of one day.)

(b) If tomorrows weather depended on the last three days of Smalltown weather, how many states will be needed to model Smalltowns weather as a Markov chain?

Solution