Assume three binary random variables a, b, c 2 f0, 1g have the following joint distribution: By

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Assume three binary random variables

a, b, c 2 f0, 1g have the following joint distribution:

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By direct evaluation, show that this distribution has the property that a and c are marginally independent (i.e., p¹a, cº = p¹aºp¹cº), but a and c become dependent when conditioned on b (i.e., p¹a, cjbº , p¹ajbºp¹cjbº).
Based on this joint distribution, draw all possible directed graphs for

a, b,

c, and compute all conditional probabilities for each graph.

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