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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 = [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 w; to wŋ, Bi̟j is the probability of observing the activity v¡ under the state wą.

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 = [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 w; to wŋ, Bi̟j is the probability of observing the activity v¡ under the state wą.

Elementary Linear Algebra (MindTap Course List)
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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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 0 = [V2, V2, V1, V3] of your friend over the past four days, where Aij is the transition probability from wito wj, Bij is the probability of observing the activity v¡ under the state w¡. [0.3 0.2 0.5 A = 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
Transcribed Image Text: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 0 = [V2, V2, V1, V3] of your friend over the past four days, where Aij is the transition probability from wito wj, Bij is the probability of observing the activity v¡ under the state w¡. [0.3 0.2 0.5 A = 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
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