Consider an example of a Bayesian belief network on a CS student getting placement in an MNC company. Event are $\{$Admission to BE$($A$\_$BE$),$ Completion of BE$($C$\_$BE$),$ Good CGPA $($CGPA$),$ Short Listed for Interview $($SLI$),$ Good Performance in Interview $($GPI$),$ Selected for Job $($SJ$)\}$

a$.$ Construct the Bayesian belief network with above nodes and related edges. Each node representing an event and connection between nodes represents the dependency between nodes. Show suitable pre$-$conditions and their connection suitably. Also mention prior proabality or conditional probability for each node.

b$.$ Write the equation for joint proability P$($SJ$,$ GPI, SLI, CGPA,C$\_$BE$,$ A$\_$BE$)$

c$.$ Write probability estimation equations for unconditional $P(SJ)$ using chain rule on the above$-$constructed network.