Average of a Curve ≠ Curve of the Average
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Average of a Curve ≠ Curve of the Average
Take a convex curve and draw a straight chord between two of its points. The midpoint of that chord is the average of the curve, but the curve evaluated at the average input sits lower down — and that stubborn vertical gap is Jensen's inequality, E[f(X)] ≥ f(E[X]). The average of a curve is simply not the curve of the average. #shorts ...
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