The belief network for the following questions is given below:
Q1: Which variables must be independent of A given C and S according to the belief network above?
My ans:
Since C is given, there is no active trail through A-C-D, hence D is independent of A.
Since C is given, there is an active trail through A-C-B, hence B may be dependent on A.
Since B may be dependent on A and E is dependent on B, E may be dependent on A.
Therefore, the only variable independent of A is D.
Q2: Which variables must be independent of A given D and S according to the belief network above?
My ans:
C is dependent on A.
Since D is given, there is no active trail through C-D-E.
There is no active trail through A-C-B.
Therefore, both B and E are independent of A.
Would really appreciate it if someone can verify whether my reasoning and answers are correct. Thank you for your help in advance.