Exercise 14.5

Consider the Bayesian network in Figure burglary-figure.

1. If no evidence is observed, are ${Burglary}$ and ${Earthquake}$ independent? Prove this from the numerical semantics and from the topological semantics.

2. If we observe ${Alarm}{true}$, are ${Burglary}$ and ${Earthquake}$ independent? Justify your answer by calculating whether the probabilities involved satisfy the definition of conditional independence.