Oh, yes, well spotted... -- APG.
Sent: Monday, February 22, 2016 at 5:25 PM From: "Dan Asimov" <asimov@msri.org> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] names for some well known facts
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."
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