Does this work? X = 1 with probability 0.5, 0 with probability 0.5 Y = 0 when X = 1, 1 when X = 0 (for the \omega for which X(\omega) = 1, Y(\omega) = 0). The

Does this work? X = 1 with probability 0.5, 0 with probability 0.5 Y = 0 when X = 1, 1 when X = 0 (for the \omega for which X(\omega) = 1, Y(\omega) = 0). They're both bernoulli distributions with p=0.5 (i.e. they follow the same distribution) and P(X=Y) = 0