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May 25, 2012 at 1:35 vote accept Tim
May 25, 2012 at 1:30 comment added Douglas Zare The distance between the point $y$ and the set $X$ is $d(y,X) = \inf_{x \in X} d(y,x)$. Then $r_X^2$ can be defined as the average of the square of the distance to $X$. This is no longer a quadratic polynomial so it can't be computed as easily as $(x-\mu)^2 + \sigma^2$, but the inequality still holds.
May 25, 2012 at 1:01 comment added Tim Thanks! How is $r_x^2$ defined when x is a set?
May 25, 2012 at 0:37 history answered Douglas Zare CC BY-SA 3.0