Exercise 3.4. Consider the Chest Clinic belief network in figure(3.15). Calculate by hand the values for

p(d), p(d|s = true), p(d|s = false). The table values are:

p(a = tr) = 0.01 p(s = tr) = 0.5

p(t = tr|a = tr) = 0.05 p(t = tr|a = fa) = 0.01

p(l = tr|s = tr) = 0.1 p(l = tr|s = fa) = 0.01

p(b = tr|s = tr) = 0.6 p(b = tr|s = fa) = 0.3

p(x = tr|e = tr) = 0.98 p(x = tr|e = fa) = 0.05

p(d = tr|e = tr; b = tr) = 0.9 p(d = tr|e = tr; b = fa) = 0.7

p(d = tr|e = fa; b = tr) = 0.8 p(d = tr|e = fa; b = fa) = 0.1

p(e = tr|t; l) = 0 only if both t and l are fa, 1 otherwise.

a: = Peeitiw Iiiray d = Dyapnea [Shortnem of breath} e = Either Tuberculosis or Lung Cancer t = Thbereuimie I = Lung Canoe: I: = Bronchitis o = Visited Asia. 5 = Smoker Figime 3.15: Belief netwk structure for the Chest. Clinic example Exercise 3.4. Consider the Cheat CHI-lie belief network in gfJjS. Calculate by hand the values for pt}, p[d|s = tr}, p{d|s = far]. The table values are: pfa = If) = lll pf: = If} = [LE pft = Trla = tr} = [UH p\" = rrla = fa} = {101 p = trls = tr} = Ill p = trls = fa] = {101 pit: = [:15 = tr} = [LE pH: = le = fa} = {13 pin: = Hie = If] = [LEE p[:: = l'J'Ie = fa} = {105 p[r=tr1e=tr,b=tr}| =03 p[d=rr|e=tr,b=fa] =11? pfe=rr1=e,b=rr} =u.e p[d=rr12=fa,tl=fa} =n.1 p{e= Ult) = [I only if both t and I are fa, I otherwise