### Artificial IntelligenceAIMA Exercises

This exercise investigates the way in which conditional independence relationships affect the amount of information needed for probabilistic calculations.
1. Suppose we wish to calculate $P(he_1,e_2)$ and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation?
1. ${\textbf{P}}(E_1,E_2)$, ${\textbf{P}}(H)$, ${\textbf{P}}(E_1H)$, ${\textbf{P}}(E_2H)$ 2. ${\textbf{P}}(E_1,E_2)$, ${\textbf{P}}(H)$, ${\textbf{P}}(E_1,E_2H)$
3. ${\textbf{P}}(H)$, ${\textbf{P}}(E_1H)$, ${\textbf{P}}(E_2H)$
2. Suppose we know that ${\textbf{P}}(E_1H,E_2)={\textbf{P}}(E_1H)$ for all values of $H$, $E_1$, $E_2$. Now which of the three sets are sufficient?

This exercise investigates the way in which conditional independence relationships affect the amount of information needed for probabilistic calculations.
1. Suppose we wish to calculate $P(he_1,e_2)$ and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation?
1. ${\textbf{P}}(E_1,E_2)$, ${\textbf{P}}(H)$, ${\textbf{P}}(E_1H)$, ${\textbf{P}}(E_2H)$ 2. ${\textbf{P}}(E_1,E_2)$, ${\textbf{P}}(H)$, ${\textbf{P}}(E_1,E_2H)$
3. ${\textbf{P}}(H)$, ${\textbf{P}}(E_1H)$, ${\textbf{P}}(E_2H)$
2. Suppose we know that ${\textbf{P}}(E_1H,E_2)={\textbf{P}}(E_1H)$ for all values of $H$, $E_1$, $E_2$. Now which of the three sets are sufficient?

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