Consider the following Bayesian Network describing the probable

causes of Arctic Melting. Note that only free parameters are given, others can be

inferred using the constraints. As an example $($just so the tables are understood

correctly: P$($T $=$ High$|$A $=$ Low, F $=$ No$)=0\mathrm{.}2)$

$($a$)[2$ points$]$ Write the Joint Density function: P$($W$,$ A$,$ F$,$ S$,$ T$,$ M$)$ given the Bayesian

Network.

$($b$)[4$ points$]$ What is the probability that Arctic will Melt if Water and Air pollution

are high but there is no Solar Flare?

$($c$)[4$ points$]$ If we know there are no Solar Flares and the Temperature is still high,

what is the probability that Air Pollution is High?