$1.$ What are the three most widely used classes of Bayesian Networks that are based on distributional assumptions?

$2.($TRUE or FALSE$)$

If two BNs have the same moral graph, then they are probabilistically equivalent.

$3.($TRUE or FALSE$)$

In a Conditional Gaussian BN$,$ a continuous node can have a discrete parent.

$4.($TRUE or FALSE$)$

In a Conditional Gaussian BN$,$ a discrete node can have a continuous parent.

$5.$ What is a local distribution? Provide an example.

$6.$ Describe two limitations of score$-$based structural learning for BNs$.$

$7.$ Describe two limitations of constraint$-$based structural learning for BNs$.$

$8.$ Consider the DAG for the survey studied in Chapter $1($Figure $1\mathrm{.}1).$

$($a$)$ List the parents and the children of each node.

$($b$)$ Identify any v$-$structures.

$1$

June $2024$ Bayesian Networks in R

$($c$)$ Identify any serial connections.

$($d$)$ Add an arc from Age to Occupation, and another arc from Travel to Education. Is the resulting graph still a valid BN$?$ If not, why?