1. Consider the marginal probability over C2 = {A1,2, A2,2, A3,2, A4,2} in the 4 × 4 grid network. Show that, if we assume general potentials, this marginal probability does not satisfy any conditional independencies.

2. Consider a clique tree T that is constructed from a run of variable elimination over a Gibbs distribution P’Φ, as described in section 10.1.2. Let Si,j be a sepset in the clique tree. Show that, for general potentials, P’Φ does not satisfy any conditional independencies relative to the marginal distribution over Si,j.


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