Remark On Variance Bounds
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It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
💡 Research Summary
The paper “Remark On Variance Bounds” revisits a classic variance decomposition formula for the union of two independent samples and shows how this single identity can be used to derive a number of well‑known variance lower‑bound inequalities in a remarkably concise way. The basic identity (1.1) states that for two disjoint samples X and Y of sizes n₁ and n₂ with means (\bar X,\bar Y) and variances (S^2_{n_1}, S^2_{n_2}), the variance of the combined sample of size (n_1+n_2) is
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