Consider the following Bayesian Network:

a$)$ Write an expression for the joint probability distribution of the above Bayesian Network. Briefly explain how you determined the expression.

b$)$ Suppose the domain of each variable in the above Bayesian Network contains six values. How many rows would be present in the local conditional probability tables associated with the following variables:

i$.$ D

ii$.$ E

iii. F

Justify your answer for the number of rows in each case.