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 day t is 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 F is the thermometer reading. We W, W; W, F1 F2 F3 W. Wo P(Wo) We P(WW1) high W P(FW) 0.7 0.3 sun sun 0.8 sun 0.9 rain 0.2 low high rain low sun sun sun rain 0.1 sun rain 0.3 0.2 rain rain 0.7 rain 0.8 1. From the transition model, we can compute P(W;-sun) - 0.75, P(W;-rain) -0.25. When Mary observed F-high, what is the probability P(W; sun | F1•high)? Answer: 2. From the transition model, we can compute P(W2-sun) - 0.675, P(Wzerain) -0.375. But we want to predict tomorrow's weather based on observation. What is P(W2-sun | F;-high)? Answer: 3. Given P(wf. f) for all w, find P(W,|f. f). Answer:

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 day t is 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 F is the thermometer reading. We W, W; W, F1 F2 F3 W. Wo P(Wo) We P(WW1) high W P(FW) 0.7 0.3 sun sun 0.8 sun 0.9 rain 0.2 low high rain low sun sun sun rain 0.1 sun rain 0.3 0.2 rain rain 0.7 rain 0.8 1. From the transition model, we can compute P(W;-sun) - 0.75, P(W;-rain) -0.25. When Mary observed F-high, what is the probability P(W; sun | F1•high)? Answer: 2. From the transition model, we can compute P(W2-sun) - 0.675, P(Wzerain) -0.375. But we want to predict tomorrow's weather based on observation. What is P(W2-sun | F;-high)? Answer: 3. Given P(wf. f) for all w, find P(W,|f. f). Answer:

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...

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