A monotonicity property of variances
Aldaz, J. M.
Original · EN
We prove that variances of non-negative random variables have the following monotonicity property: For all 0 < r < s ≤ 1, and all 0 ≤ X ∈ L², we have Var(Xʳ)¹/ʳ ≤ Var(Xˢ)¹/ˢ. We also discuss the real valued case.
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