3. {14 points} In HW 4, we considered naive Bayes models, where the observed dimensions as; (1' = 1, . . . ,D) are independent, conditioned on the class 2 E {1, . . . , K}. {a} ( points].l Draw a directed graph representing the joint probabilitf,r distribution over the variables 2:1, . . . ,ID and 2. There should be one node for each of the D + 1 variables. (b) (4 points) Write the joint distribution Prl, . . . , :1: D, 2} in terms of a product of condi- tional distributions, one for each node in the graph. [c] (4 points) Are :31, . . . , :1: D independent? Why