Question: Show that the statement of conditional independence is equivalent to each of the statements P(X,Y |Z) = P(X Z)P(Y | Z) P(X |Y, Z) =

Show that the statement of conditional independence

P(X,Y |Z) = P(X Z)P(Y | Z)


is equivalent to each of the statements

P(X |Y, Z) = P(X|Z) and P(BX,Z)= P(Y|Z). and P(B|X, Z) = P(Y | Z).

P(X,Y |Z) = P(X Z)P(Y | Z) P(X |Y, Z) = P(X|Z) and P(BX,Z)= P(Y|Z). and P(B|X, Z) = P(Y | Z).

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