#factorisation

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2 questions · 2 min · score and explanations at the end

Q 1 / 2Score 0 / 0

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Which condition on a joint pdf/pmf $p(x, y, z)$ is equivalent to $x \perp y \mid z$ ?

$p(x, y, z) = a(x, y)\, b(z)$ for some non-negative functions $a$ and $b$ 1
$p(x, y, z) = p(x)\, p(y)\, p(z \mid x, y)$ 2
$p(x, y, z) = a(x, z)\, b(y, z)$ for some non-negative functions $a$ and $b$ 3
$p(x, y \mid z) = p(x)\, p(y)$ 4

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