This intuition about what variables are independent of other
variables is formalized by what is called *d-separation*.
You are not expected to know about d-separation to answer the question.

Consider the following belief network:

Suppose

*I(C,G|{})*is true, as*P(C|G)=P(C)*by the definition of a belief network.*I(C,G|{F})*is false, as knowing something about*C*could explain why*F*had its observed value, which in turn would explain away*G*as a cause for*F*'s observed value. [Remember, you just need to imagine one probability distribution to make the independence assertion false.]*I(F,I|{G})*is true because the only way that knowledge of*F*can affect*I*is by changing our belief in*G*, but we are given the value for*G*.

- Is
*I(A,F|{})*true or false? Explain. - Is
*I(A,F|{C})*true or false? Explain. - Is
*I(A,F|{D,C})*true or false? Explain. - Is
*I(C,F|{D,E})*true or false? Explain. - Is
*I(G,J|{F})*true or false? Explain. - Is
*I(G,J|{I})*true or false? Explain. - Is
*I(F,J|{I})*true or false? Explain. - Is
*I(A,J|{I})*true or false? Explain. - Is
*I(A,J|{I,F})*true or false? Explain.

Computational Intelligence online material, ©David Poole, Alan Mackworth and Randy Goebel, 1999