Question

Data available from Weather Underground indicates that in Minneapolis in 2017, if there was pre cipitation on a given day, then there was approximately a 25% chance of precipitation the next day. On the other hand, if a given day had no precipitation, then there was a 30% chance there was no precipitation the next day. We want to use this data to forecast weather for this year (a) (6 points) Set up a Markov chain model to determine the probability of precipitation on any given day. Define appropriate variables, and write down an appropriate transition probability matrix. Without doing any calculations, which state should be most likely to occur? (b) (14 points) Now assume that the two states (precipitation and no precipitation) that have duration possibly longer or shorter than a day. Let the average duration of precipitation be 1/A = 2 days, and the average duration of no precipitation be 1/λ = 5 days, what is the proportion of time spent in each state, assuming a steady-state distribution of 0.5 for the transition probabilities of each state? occur as events

Answer 1

solutioの: わーprecipitation on Let us denote, precipitation on a given day b j and n° pe cipitation on given dag b so from t he given informa tion in question, The transition probabilit ma tnx is 0 0.30 70 0.75 o.2s eo precipitation is most tikelg o occur b Let averag e duration of pvecipation be 2 day s aind average duration of no precipitation be Lis days. Assume steady-state clistribution of o.s fo the raosstion probobilities of each state. so Proportion of time spent in state o0-71 4 7 cnd proportion of time speatin state 4 ts 2: 0.28s