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CECS 451 Assignment 10

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CECS 451
Assignment 10
Total: 29 Points
General Instruction
• Submit your work in the Dropbox folder via BeachBoard (Not email or in class).
1. Consider the Bayes net shown in Figure 1. Write answers with a scale of 4, i.e., 0.1234.
(You don’t need to show the calculation steps.)
(a) (2 points) Calculate the value of P(b, i, ¬m, g, j).
(b) (3 points) Calculate the value of P~ (J|b, i, m).
(c) (4 points) Calculate the value of P~ (J|¬b, ¬i, m).
Figure 1: A simple Bayes net with Boolean variables.
CECS 451 Assignment 10 – Page 2 of 2
2. (6 points) In Figure 2, suppose we observe an unending sequence of days on which the
umbrella appears. As the days go by, the probability of rain on the current day increases
toward a fixed point, we expect that P~ (Rt
|u1:t) = P~ (Rt−1|u1:t−1) = hρ, 1 − ρi. Find ρ
with a scale of 4, i.e., 0.1234. (You don’t need to show the calculation steps.)
Figure 2: Bayesian network structure and conditional distributions describing the umbrella
world. The transition model is P~ (R|Rt−1) and the sensor model is P~ (U|Rt).
3. A professor wants to know if students are getting enough sleep. Each day, the professor
observes whether they have red eyes. The professor has the following domain theory:
• The prior probability of getting enough sleep, with no observations, is 0.7.
• The probability of getting enough sleep on night t is 0.8 given that the student got
enough sleep the previous night, and 0.3 if not.
• The probability of having red eyes is 0.2 if the student got enough sleep, and 0.7 if
not.
(a) (6 points) Formulate this information as a hidden Markov model. Give a Bayesian
network and conditional distributions.
(b) (8 points) Consider the following evidences, and compute P~ (ES2|~e1:2) with a scale
of 4, i.e., 0.1234. (You don’t need to show the calculation steps.)
• ~e1 = red eyes
• ~e2 = not red eyes

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