Consider the problem of predicting a lung disease.

Assume that a Pulmonologist has constructed the following bayesian network, where:

A = Family History = {Yes, No}

B = Asbestos Exposure = {Ideal, Pre-High, High, Very High}

C = Smoking = {Yes, No}

D = Asthma = {Yes, No} 2

E = Lung Cancer = {Yes, No}

F = Wheezing = {No, Inhale, Exhale, Both}

G = Breathing Trouble = {No, Slight, High}

H = Chest Pain = {No, Slight, High}

	P(d1|ai,bj,ck)	P(d2|ai,bj,ck)		P(e1|ai,bj,ck)	P(e2|ai,bj,ck)
a1, b1, c1	0.25	0.75	a1, b1, c1	0.111	0.889
a1, b1, c2	0.111	0.889	a1, b1, c2	0.833	0.167
a1, b2 c1	0.1	0.9	a1, b2 c1	0.307	0.693
a1, b2, c2	0.833	0.167	a1, b2, c2	0.5	0.5
a1, b3, c1	0.285	0.715	a1, b3, c1	0.4	0.6
a1, b3, c2	0.307	0.693	a1, b3, c2	0.25	0.75
a1, b4, c1	0.454	0.546	a1, b4, c1	0.692	0.308
a1, b4, c2	0.5	0.5	a1, b4, c2	0.5	0.5
a2, b1, c1	0.571	0.429	a2, b1, c1	0.428	0.572
a2, b1, c2	0.4	0.6	a2, b1, c2	0.818	0.182
a2, b2 c1	0.5	0.5	a2, b2 c1	0.181	0.819
a2, b2, c2	0.25	0.75	a2, b2, c2	0.5	0.5
a2, b3, c1	0.875	0.125	a2, b3, c1	0.333	0.667
a2, b3, c2	0.692	0.308	a2, b3, c2	0.416	0.584
a2, b4, c1	0.181	0.819	a2, b4, c1	0.333	0.667
a2, b4, c2	0.5	0.5	a2, b4, c2	0.75	0.25

	P(g1|di,ej)	P(g2|di,ej)	P(g3|di,ej)			P(h1|di,ej)	P(h2|di,ej)	P(h3|di,ej)
d1,e1	0.15	0.45	0.4		d1,e1	0.307	0.076	0.617
d1,e2	0.307	0.076	0.617		d1,e2	0.125	0.25	0.625
d2,e1	0.5	0.444	0.56		d2,e1	0.09	0.09	0.82
d2,e2	0.125	0.25	0.625		d2,e2	0.571	0.142	0.287

	P(f1|di,ej)	P(f2|di,ej)	P(f3|di,ej)	P(f4|di,ej)
d1,e1	0.055	0.055	0.5	0.39
d1,e2	0.086	0.391	0.217	0.306
d2,e1	0.296	0.074	0.296	0.334
d2,e2	0.15	0.2	0.4	0.25

Given the Bayesian Network above, First write the expression to find the joint probability of all random variable. After that for the given evidences, write the expression with factors with marginalization. Note, We just need an expression. Please do not calculate the joint probability.

(a) Write an expression for joint probability when we observe that person is having Slight Breathing Difficulties and having High Chest Pain.

(b) Write an expression for joint probability when we observe that the Person smokes, and we have the family history of the person.

(c) Write an expression for joint probability when we observe that the person has wheezing while inhaling and exhaling both. We also observe that the person has high exposure to Asbestos.