D Question 7 15 pts Mary stays in her graduate student office in the basement for days. She has made up her mind not lea

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D Question 7 15 Pts Mary Stays In Her Graduate Student Office In The Basement For Days She Has Made Up Her Mind Not Lea 1 (57.33 KiB) Viewed 18 times

D Question 7 15 pts Mary stays in her graduate student office in the basement for days. She has made up her mind not leaving her office until she completes her research project. However, she wants to know what weather is like outside. There is a thermometer in her office, which is the only source of information that Mary can obtain. The following Hidden Markov Model describes the weather at daytis independent to the weather before day t-1 given the weather at day t-1. The initial transition and sensor model is given in the following where W is the weather outside and Fis the thermometer reading. Wo W W W F F2 F3 Wo P(W) sun 0.9 rain 0. W W P(WAW.-1) sun sun 0.8 rain sun 0.2 sun rain 0.3 rain rain 0.7 F WE P(FW) high sun 0.7 low sun 0.3 high rain 0.2 low rain 0.8 1. From the transition model, we can compute P/W,-sun) = 0.75, P/W-rain) -0.25. When Mary observed Fy=high, what is the probability P/W,-sun | Fy=high)? Answer: 2. From the transition model, we can compute P(W2-sun) = 0.675, P[Wywrain) -0,375. But we want to predict tomorrow's weather based on observation. What is P/ Wz-sun | Fy=high)? Answer: 3. Given Plwilf..... f) for all w, find P[W-1 | ft. -... f.). Answer: