Question: Let f be a p.f. for a discrete distribution. Suppose that f (x) = 0 for x [0, 1]. Prove that the variance of

Let f be a p.f. for a discrete distribution. Suppose that f (x) = 0 for x ∉ [0, 1]. Prove that the variance of this distribution is at most 1/4. Prove that there is a distribution supported on just the two points {0, 1} that has variance at least as large as f does and then prove that the variance of a distribution supported on {0, 1} is at most 1/4.

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