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Q2. People often decide their outdoor activities according to the weather conditions. Suppose you have a friend in London, where the weather conditions, denoted by W = (W1, W2, W3), is unknown. His activities option, denoted by V = (v₁, V2, V3), is decided by the weather conditions. The initial state of the weather is 7 = [0.3, 0.4, 0.3]. Given the Hidden Markov model 0 = (A, B, T), calculate the probability that you observe a specific activity sequence O [V2, V2, V1, V3] of your friend over the past four days, where A₁, is the transition probability from wi to wj, Bij is the probability of observing the activity v, under the state wi. = A = [0.3 0.2 0.5] 0.1 0.4 0.5 B 0.2 0.5 0.3 = [0.4 0.5 0.1] 0.2 0.4 0.4 0.3 0.1 0.6

Q2. People often decide their outdoor activities according to the weather conditions. Suppose you have a friend in London, where the weather conditions, denoted by W = (W1, W2, W3), is unknown. His activities option, denoted by V = (v₁, V2, V3), is decided by the weather conditions. The initial state of the weather is 7 = [0.3, 0.4, 0.3]. Given the Hidden Markov model 0 = (A, B, T), calculate the probability that you observe a specific activity sequence O [V2, V2, V1, V3] of your friend over the past four days, where A₁, is the transition probability from wi to wj, Bij is the probability of observing the activity v, under the state wi. = A = [0.3 0.2 0.5] 0.1 0.4 0.5 B 0.2 0.5 0.3 = [0.4 0.5 0.1] 0.2 0.4 0.4 0.3 0.1 0.6

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q2. People often decide their outdoor activities according to the weather conditions. Suppose you have a friend in London, where the weather conditions, denoted by W = (W1, W2, W3), is unknown. His activities option, denoted by V = (v₁, V2, V3), is decided by the weather conditions. The initial state of the weather is π = [0.3, 0.4, 0.3]. Given the Hidden Markov model 0 (A, B, π), calculate the probability that you observe a specific activity sequence O [V2, V2, V1, V3] of your friend over the past four days, where Aį, is the transition probability from wi to wj, Bij is the probability of observing the activity v; under the state wi. A = [0.3 0.2 0.5] 0.1 0.4 0.5 0.2 0.5 0.3 B = = [0.4 0.5 0.1] 0.2 0.4 0.4 0.3 0.1 0.6 =
Transcribed Image Text:Q2. People often decide their outdoor activities according to the weather conditions. Suppose you have a friend in London, where the weather conditions, denoted by W = (W1, W2, W3), is unknown. His activities option, denoted by V = (v₁, V2, V3), is decided by the weather conditions. The initial state of the weather is π = [0.3, 0.4, 0.3]. Given the Hidden Markov model 0 (A, B, π), calculate the probability that you observe a specific activity sequence O [V2, V2, V1, V3] of your friend over the past four days, where Aį, is the transition probability from wi to wj, Bij is the probability of observing the activity v; under the state wi. A = [0.3 0.2 0.5] 0.1 0.4 0.5 0.2 0.5 0.3 B = = [0.4 0.5 0.1] 0.2 0.4 0.4 0.3 0.1 0.6 =
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