d-separation

a)

[2 P] In Figure 1 you can see a Bayesian network which is used for the diagnosis of lung cancer and tuberculosis. Check if the following conditional independence assumptions are true or false.²

(i)

$tuberculosis \perp smoking \vert dyspnea$

(ii)

$lung cancer \perp bronchitis \vert smoking$

(iii)

$visit\:to\:Asia \perp smoking \vert lung cancer$

(iv)

$visit\:to\:Asia \perp smoking \vert lung cancer, dyspnea$

Figure 1: Bayesian network for the diagnosis of lung cancer and tuberculosis.