In the nuclear power station that Malt-O-Meal has hidden underground, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the core temperature. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), FG (gauge is faulty), and the multivalued nodes G (gauge reading) and T (actual core temperature).
1. Draw a Bayesian network for this domain, given that the gauge is more likely to fail when the core temperature gets too high.
2. Is your network a polytree?
3. Suppose there are just two possible actual and measured temperatures, Normal and High, and that the gauge gives the incorrect temperature x% of the time when it is working, but y% of the time when it is faulty. Give the conditional probability table associated with G.
4. Suppose the alarm works unless it is faulty, in which case it never goes off. Give the conditional probability table associated with A.
5. Suppose the alarm and gauge are working, and the alarm sounds. What is the probability that the core temperature is too high? Your answer should be in terms of x, y, and any other values that would be in a CPT in the Bayesian network. If you need to use values which we have not filled in, create new variables to represent them (for example z, w, q, etc.).