Question: 3. (14 points) In HW 4, we considered nuinc Buycs models, where thc observed dimensions 1, , D) are independent, conditioned on the class

3. (14 points) In HW 4, we considered nuinc Buycs models, where

3. (14 points) In HW 4, we considered nuinc Buycs models, where thc observed dimensions 1, , D) are independent, conditioned on the class z C {1, , K}. (a) (6 points) Draw a directed graph representing thc joint probability distribution over thc variables , .ED and z. There should be one node for each of thc D 1 variables. (b) (4 points) Write the joint distribution P(TI,... , xn, ' z) in terms of a product of condi- t,ional distributions, one for each node in the graph. (C) (4 points) Arc , independent? Why?

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