Question: 1. [20 Points] Below (sew table) is the joint probability distribution over three Boolean variables (Z, X, and Y True True True True False False

1. [20 Points] Below (sew table) is the joint probability distribution

1. [20 Points] Below (sew table) is the joint probability distribution over three Boolean variables (Z, X, and Y True True True True False False False False True True False False True True False False True False True False True False True False P(X,Y 0.018 0.002 0.072 0.008 0.252 0.378 0.108 0.162 a. Is Z conditionally independent of Y given X? Why or why not? b. Consider your answers above. Draw a Bayesian network (CPTs and graph) that represents the above joint probability distribution more compactly. In other words, your network should have fewer independent parameters than the full joint distribution. How many independent parameters are in the full joint distribution? Consider the network you drew above. How many independent parameters does it have? c

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