Consider a Bayes net over the random variables A, B, C, D, E with the structure shown in Figure S13.2, with full joint distribution P(A, B, C, D, E). 

a. Consider the marginal distribution P(A, B, D, E) = Σc P(A, B, c, D, E), where C was eliminated. Draw the minimal Bayes net that is guaranteed to be able to represent this distribution. 

b. Assume we are given an observation: A = a. Draw the minimal Bayes net that is guaranteed to be able to represent the distribution P' (B, C, D, E) = P(B, C, D, E | A = a).

c. Assume we are given two observations: D = d, E = e. Draw the minimal Bayes net that is guaranteed to be able to represent the distribution P 00(A, B, C) = P(A, B, C | D = d, E = e).

Figure S13.2

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A D C B E