19.4 (Courtesy of Judea Pearl, a resident of earthquake country.) The belief network shown here formalizes the following situation: you have a new burglar alarm installed at home. It is fairly reliable at detecting a burglary, but also responds on occasion to minor earthquakes. You also have two neighbors, John and Mary, who have promised to call you at work when they hear the alarm. John quite reliably calls when he hears the alarm, but sometimes confuses the telephone ringing with the alarm and calls then too. Mary, on the other hand, likes rather loud music and sometimes misses the alarm altogether. P(B) = .001 p(E)= = .002 Burglary Earthquake P(A/B,E) = .98 p(A|B2E) = .95 p(Al-B,E) = .29 p(AT-B, -E) = .001 Alarm JohnCalls MaryCalls p(J/A) = .95 p(JI-A) = .01 p(MA) = .70 p(MMA)= .01 To exercise your ability to work with joint probabilities as defined by belief networks, calculate the joint probability that neither John nor Mary calls and that there is both an earthquake and a burglary. That is, calculate p(-J, -M, B, E). 19.4 (Courtesy of Judea Pearl, a resident of earthquake country.) The belief network shown here formalizes the following situation: you have a new burglar alarm installed at home. It is fairly reliable at detecting a burglary, but also responds on occasion to minor earthquakes. You also have two neighbors, John and Mary, who have promised to call you at work when they hear the alarm. John quite reliably calls when he hears the alarm, but sometimes confuses the telephone ringing with the alarm and calls then too. Mary, on the other hand, likes rather loud music and sometimes misses the alarm altogether. P(B) = .001 p(E)= = .002 Burglary Earthquake P(A/B,E) = .98 p(A|B2E) = .95 p(Al-B,E) = .29 p(AT-B, -E) = .001 Alarm JohnCalls MaryCalls p(J/A) = .95 p(JI-A) = .01 p(MA) = .70 p(MMA)= .01 To exercise your ability to work with joint probabilities as defined by belief networks, calculate the joint probability that neither John nor Mary calls and that there is both an earthquake and a burglary. That is, calculate p(-J, -M, B, E)