Use d$-$separation to determine whether the following conditional independencies are implied by the structure of this Bayes net. Explain your answer by specifying which path is$/$isn$\text{'}$t blocked. The notation X perpendicular Z space vertical line space Y means that X is conditionally independent of Z given that the value of Y is known.

a$)$ Is A perpendicular I space vertical line space empty set implied by the structure of the Bayes net?

$-$ Is the path A$-$E$-$I blocked? Yes or no$?$

$-$ Is the path A$-$B$-$C$-$G$-$F$-$E$-$I blocked? Yes or no$?$

QUESTION $16$

b$)$ Is A perpendicular I space vertical line space G implied by the structure of the Bayes net?

$-$ Is the path A$-$E$-$I blocked? Yes or no$?$

$-$ Is the path A$-$B$-$C$-$G$-$F$-$E$-$I blocked? Yes or no$?$

QUESTION $17$

c$)$ Is J perpendicular G space vertical line space F implied by the structure of the Bayes net?

$-$ Is the path J$-$I$-$E$-$F$-$G blocked? Yes or no$?$

$-$ Is the path J$-$I$-$E$-$A$-$B$-$C$-$G blocked? Yes or no$?$

QUESTION $18$

d$)$ Is J perpendicular M space vertical line space K comma L implied by the structure of the Bayes net?

$-$ Is the path J$-$K$-$M blocked? Yes or no$?$

$-$ Is the path J$-$L$-$M blocked? Yes or no$?$

QUESTION $19$

e$)$ Is E perpendicular C space vertical line space A comma G implied by the structure of the Bayes net?

$-$ Is the path E$-$A$-$B$-$C blocked? Yes or no$?$

$-$ Is the path E$-$F$-$G$-$C blocked? Yes or no$?$

QUESTION $20$

f$)$ Is E perpendicular C space vertical line space A implied by the structure of the Bayes net?

$-$ Is the path E$-$A$-$B$-$C blocked? Yes or no$?$

$-$ Is the path E$-$F$-$G$-$C blocked? Yes or no$?$