$($b$)[5$ points$]$ Draw a belief network that is consistent with a joint distribution that factors

as P$($A$,$ B$,$ C$,$ D$,$ E$)=$ P$($A$)$P$($B$|$A$)$P$($C$)$P$($D$|$A$,$ C$)$P$($E$|$B$,$ C$,$ D$).$

$($c$)[5$ points$]$ Draw another belief network that is different from the network of question $(2$b$)$

but also consistent with the factoring P$($A$,$ B$,$ C$,$ D$,$ E$)=$ P$($A$)$P$($B$|$A$)$P$($C$)$P$($D$|$A$,$ C$)$P$($E$|$B$,$ C$,$ D$).$

$($i$.$e$.,$ a different belief network that is guaranteed to be correct for any joint distribution

that can be correctly represented by this factoring$).$

$($d$)[3$ points$]$ Suppose that every random variable in the joint distribution of question $(2$b$)$

has a domain containing $8$ elements. How many rows are needed to list the full joint

distribution in an explicit table?

$($e$)[7$ points$]$ Suppose that every random variable in the joint distribution of question $(2$b$)$

has a domain containing $8$ elements. How many rows in total are needed to list the

conditional probability tables for your belief network representation? Only Answer D and E please