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)
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
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d860cd5-2859-4da0-be1a-b0f5f49f917c%2Fee8ddf18-1f28-4576-937d-9aba306bc1cb%2Fw92h62p_processed.jpeg&w=3840&q=75)
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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