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Is $P(X_1,\dots,X_N \mid C)*P(C)$ equal to $P(X_1 \mid C) * P(X_2,\dots,X_N\mid C) * P(C)$?

I can't find the proof by myself.

EDIT

I found the associated article on wikipedia (Conditional Independence).

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    not in general. If and only if the events are conditionally independent. – 2017-01-28

1 Answers 1

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No -- only if $X_1$ is conditionally independent of $X_2,\ldots,X_N$ given $C$.