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 (c) (4 points) Calculate the value of
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 . 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 ) and the sensor model is
3. A professor wants to know if students are getting enough sleep. Each day, the professorobserves 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 Bayesiannetwork and conditional distributions.
(b) (8 points) Consider the following evidences, and compute ) 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
