22 Feb
2016
22 Feb
'16
10:26 a.m.
Maybe the second term should have the ^2 outside the || ? —Dan
On Feb 22, 2016, at 3:58 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
A generalisation is that:
|X - E(X)|^2 + |Y - E(Y)^2| + |E(X) - E(Y)|^2 = E(|X - Y|^2)
where X and Y are two independent random variables on the same inner product space. Equivalently:
"The mean squared distance between two distributions is equal to the sum of their variances and the squared distance between their barycentres."