### Artificial IntelligenceAIMA Exercises

Let $X$, $Y$, $Z$ be Boolean random variables. Label the eight entries in the joint distribution ${\textbf{P}}(X,Y,Z)$ as $a$ through $h$. Express the statement that $X$ and $Y$ are conditionally independent given $Z$, as a set of equations relating $a$ through $h$. How many nonredundantequations are there?

Let $X$, $Y$, $Z$ be Boolean random variables. Label the eight entries in the joint distribution ${\textbf{P}}(X,Y,Z)$ as $a$ through $h$. Express the statement that $X$ and $Y$ are conditionally independent given $Z$, as a set of equations relating $a$ through $h$. How many nonredundantequations are there?

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