1. Let G 2 (ME) be a DAG. We say that an edge 3' >j E E is a covered edge if and only if 11'3- = in; U {i} (where in: is the set of parents ofa node i E V). Let Gd 2 (V, E'), with EF 2 (E \\ {1' > j}) U {j > i}. Prove that a distribution Mm) factorizes according to G if and only if it factorizes according to G". 2. Let G be a directed tree and GI its corresponding undirected tree (where the orientation of the edges is ignored). Recall that by denition of a directed tree, G does not contain any v-slructure. Prove that a distribution ptr) factorizes according to G if and only if it factorizes according to G