Questions 1-6 refer to the Bayesian network in Figure 1. Questions 7 and 8 refer to the Bayesian network in Figure 2.
Figure 1: A Bayesian network graph establishing relations between various car problems and their causes.
On the network shown in Figure 1, consider the event E = "battery age is less than three years". Let A = P(E | "battery dead"=true AND "no oil"=true) and B = P(E | "battery dead"=true AND "no oil"=false). Which of the following three cases can possibly be true: A > B, A = B, or A < B? Why?
On the network shown in Figure 1, consider again the event E = "battery age is less than three years". Let A = P(E | "battery dead"=true AND "no oil"=true) and B = P(E | "battery dead"=true AND "starter broken"=true). Which of the following three cases can possibly be true: A > B, A = B, or A < B? Why?
The "alternator broken" event and the "fanbelt broken" event are both causes of the "no charging event." Let A = P("alternator broken"=true | "no charging"=true) and B = P("alternator broken"=true | "no charging"=true AND "fanbelt broken"=true). Which of the following three cases do you expect to be true: A > B, A = B, or A < B? Why?
On the network shown in Figure 1, the "no gas" event is a cause of the "car won't start" event. Let A = P("no gas"=true) and B = P("no gas"=true | "car won't start"=true). Which of the following three cases do you expect to be true: A > B, A = B, or A < B? Why?
On the network shown in Figure 1, suppose that:
Suppose that:
Figure 2: A Bayesian network establishing relations between events on the burglary-earthquake-alarm domain, together with complete specifications of all probability distributions.
On the network shown in Figure 2, what is the probability of the following event: burglary=false AND earthquake=true AND alarm=false AND JohnCalls=true AND MaryCalls=false.
On the network shown in Figure 2, what is the probability of the following event: earthquake=true AND alarm=false AND JohnCalls=true AND MaryCalls=false.