Consider the Bayes net shown in Figure politicsfigure.

Which of the following are asserted by the network structure?

${\textbf{P}}(B,I,M) = {\textbf{P}}(B){\textbf{P}}(I){\textbf{P}}(M)$.

${\textbf{P}}(JG) = {\textbf{P}}(JG,I)$.

${\textbf{P}}(MG,B,I) = {\textbf{P}}(MG,B,I,J)$.


Calculate the value of $P(b,i,\lnot m,g,j)$.

Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor.

A contextspecific independence (see page CSIpage) allows a variable to be independent of some of its parents given certain values of others. In addition to the usual conditional independences given by the graph structure, what contextspecific independences exist in the Bayes net in Figure politicsfigure?

Suppose we want to add the variable $P{PresidentialPardon}$ to the network; draw the new network and briefly explain any links you add.