### Artificial IntelligenceAIMA Exercises

Consider the Bayes net shown in Figure politics-figure
. 1. Which of the following are asserted by the network structure?
1. ${\textbf{P}}(B,I,M) = {\textbf{P}}(B){\textbf{P}}(I){\textbf{P}}(M)$.
2. ${\textbf{P}}(J|G) = {\textbf{P}}(J|G,I)$.
3. ${\textbf{P}}(M|G,B,I) = {\textbf{P}}(M|G,B,I,J)$.
2. Calculate the value of $P(b,i,\lnot m,g,j)$.
3. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor.
4. A context-specific independence (see page CSI-page) 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 context-specific independences exist in the Bayes net in Figure politics-figure?
5. Suppose we want to add the variable $P={PresidentialPardon}$ to the network; draw the new network and briefly explain any links you add.

Consider the Bayes net shown in Figure politics-figure
. 1. Which of the following are asserted by the network structure?
1. ${\textbf{P}}(B,I,M) = {\textbf{P}}(B){\textbf{P}}(I){\textbf{P}}(M)$.
2. ${\textbf{P}}(J|G) = {\textbf{P}}(J|G,I)$.
3. ${\textbf{P}}(M|G,B,I) = {\textbf{P}}(M|G,B,I,J)$.
2. Calculate the value of $P(b,i,\lnot m,g,j)$.
3. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor.
4. A context-specific independence (see page CSI-page) 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 context-specific independences exist in the Bayes net in Figure politics-figure?
5. Suppose we want to add the variable $P={PresidentialPardon}$ to the network; draw the new network and briefly explain any links you add.

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