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    L1 distance between empirical and true distribution for discrete distributions

    I have a discrete distribution over the set {1, \ldots, d} with a corresponding pmf P. Given a dataset with n i.i.d. samples from P, I compute the empirical distribution as Q. I want to bound from above and below E[\|P-Q\|_1]. I would think that this is something well known, but I just can't...