Task 4

Questions

Part a:

On the network shown above, what is the Markovian blanket of node L?

Part b:

On the network shown above, what is P(A, F)? How is it derived?

Part c:

On the network shown above, what is P(M, not(C) | H)? How is it derived?

Note: You do not have to use Inference by Enumeration for parts b and c.

Answers

Part a

Markovian blanket of L
Parents: G
Children: P,Q
Children's other parents: K, M

So G, P, Q, K, M

Part b

$P(A,F)=P(\frac{F}{A})P(A)$
$P(A,F)=0.8\times 0.8$
$P(A,F)=0.64$

Part c

$P(M,\mathrm{\neg }C|H)=\frac{P(M,\mathrm{\neg }C,H)}{P(H)}$

$P(M,\mathrm{\neg }C|H)=\frac{P(\frac{M}{H})\ast P(\frac{H}{\mathrm{\neg }C})\ast P(\mathrm{\neg }C)}{P(H\wedge C)+P(H\wedge \mathrm{\neg }C)}$

$P(M,\mathrm{\neg }C|H)=\frac{P(\frac{M}{H})\ast P(\frac{H}{\mathrm{\neg }C})\ast P(\mathrm{\neg }C)}{P(\frac{H}{C})P(C)+P(\frac{H}{\mathrm{\neg }C})P(\mathrm{\neg }C)}$

$P(M,\mathrm{\neg }C|H)=\frac{0.1\times 0.1\times 0.4}{0.6\times 0.6+0.1\times 0.4}$

$P(M,\mathrm{\neg }C|H)=\frac{0.004}{0.4}$

$P(M,\mathrm{\neg }C|H)=0.01$