Part B.[4pt] Given your network above, which of the following (conditional) independences hold? Briefly justify your answer in each case:
Given no evidence at all, they are independent of each other.
Using D-SEP, we can see that once SL is given, IP and LH are not independent (the "common-effect" case; since neither CM nor any of its descendants can be in the evidence for IP and LH to be independent)
Using D-Sep again, LH is indepedent of SL given CM (since the only path from LH to SL goes through CM, and it is an inter-causal path, and it gets blocked once CM is known). Another way of seeing this is that CM is the markov blanket of SL, and so given CM, SL is independent of everything else.