(Ex.3 from 3.a to 3.c in Ch12 of the book KRR) Consider the following example: The fire alarm in a building can go off if there is a fire in the building or if the alarm is tampered with by vandals. If the fire alarm goes off, this can cause crowds to gather at the front of the building and fire trucks to arrive. (a) Represent these causal links in a belief network. Let a stand for “alarm sounds,” c for “crowd gathers”, f for “fire exists”, t for “fire truck arrives”, and v for “vandalism exists”. (b) Give an example of an independence assumption that is implicit in this network. (c) What are the 10 conditional probabilities that need to be specified to fully determine the joint probability distribution? Suppose that there is a crowd in front of the building one day but that no fire trucks arrive. What is the chance that there is a fire, expressed as some function of the 10 given conditional probabilities?
(Ex.3 from 3.a to 3.c in Ch12 of the book KRR) Consider the following example:
The fire alarm in a building can go off if there is a fire in the building or if the alarm is
tampered with by vandals. If the fire alarm goes off, this can cause crowds to gather at the
front of the building and fire trucks to arrive.
(a) Represent these causal links in a belief network. Let a stand for “alarm sounds,” c for
“crowd gathers”, f for “fire exists”, t for “fire truck arrives”, and v for “vandalism exists”.
(b) Give an example of an independence assumption that is implicit in this network.
(c) What are the 10 conditional probabilities that need to be specified to fully determine the
joint probability distribution? Suppose that there is a crowd in front of the building one
day but that no fire trucks arrive. What is the chance that there is a fire, expressed as
some function of the 10 given conditional probabilities?
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