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Statistical Independence Testing

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P(A and B) = P(A) P(B)

OR

P(A|B) = P(A)

BUT, I seem to recall reading elsewhere that while an inequality can be assumed to mean DEPENDENCE, and equality may or may NOT mean independence. Is that correct? If so, how can one really PROVE independence?

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This solution explains how to check independence

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The only way to check independence is to check whether
P(A and B) = P(A) ...

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