Consider the Bayesian network in
FigureĀ 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.

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.

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.