Bayes Net Theorem

[ElistheFox]

Dear community,

I have just finished a task regarding Bayes Net Theorem but I would be glad, if someone found the time to double-checked it, since I am not 100 % sure whether it is correct.

Task:

My input graph:
R=Rain
F=Flood
...


Question n.1:
Which conditional probabilities should we add in order to get Bayes net?

P(R) ; P(B) ; P(E) ; P(F|A) ; P(A|F, B, E) ; P(S|B, E)

Question n.2:
Find two different arrangements of nodes to apply i ∈ pa(j) => no(i) < no(j)

Here I am completely lost.

Question n.3:

Perform moralization and triangularization (distinguish), arrange the handles to meet the running intersection property and create a connection tree.

Moralization: I have added two blue lines to connect F and B, B and E


Triangularization:

I have added orange line to connect A and S.



Handles:
{R,F}, {F, A, B}, {B, A, E}, {B, S, E}, {A,E,S}, {A,B,S}

Arrangement:
{A,B,S}, {A,E,S}, {B, S, E}, {B, A, E}, {F, A, B}, {R,F}

Running intersection property:

{A, B, S} ∩ {A, B, E, S} = {A,S} <= {A, B ,E}
{A, B, E} ∩ {A, B, E, S, F} = {A, B} <= {A, B, E}


Tree
BFA-BF-ABE-AS-ABS
|
AE
|
BSE

Question n.4:
Are those condtional dependencies valid? Yes or no
Rain ⊥ Earthquake yes
R ⊥ E | Flood yes
R ⊥ E | Burglary no
R ⊥ E | F, B no

If anyone helps me to correct my assignment, I would be really glad, this is my first time trying to solve this kind of problem.

Thanks!