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1. Consider this joint probability distribution P:
P(x1; y1; z1) = 0:03P(x1; y1; z2) = 0:27P(x1; y2; z1) = 0:04P(x1; y2; z2) = 0:16P(x2; y1; z1) = 0:09P(x2; y1; z2) = 0:21P(x2; y2; z1) = 0:08P(x2; y2; z2) = 0:12
(a) Determine whether P constitutes a Bayesian network with the DAG X -> Y -> Z:
(b) Determine whether P constitutes a Bayesian network with the DAG X -> Z <- Y
Give an example representing a discrete probability distribution and a continuous probability distribution. Explain why your choice is discrete and continuous.
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