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Y is a function of X, but Y can still be stochastically independent with X???

THanks

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@Yue: This is not a research-level question. Either math.stackexchange.com or stats.stackexchange.com would be ok places to ask this. Indeed, it's been answered in rather excruciating detail at the latter (stats.stackexchange.com/questions/16321) and, I believe, also at the former, though I haven't located a link there, yet. –  cardinal Mar 6 '12 at 23:43

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It could be uncorrelated but not independent.

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@taylor: Your statement is false. –  cardinal Mar 6 '12 at 23:39

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