X and Y are independent random variables with uniform distribution
$E\left[ \lVert X - Y \rVert_2^2 \right] = \frac{d}{15}\ +\frac{d(d-1)}{36}$ and $\mathrm{Var}\left[ \lVert X - Y\rVert_2^2\right] = \frac{7d}{180}$.
the maximum possible squared Euclidean distance between two points within the d-dimensional unit cube (this would be the distance between opposite corners of the cube). Why does this support the claim that in high dimensions,“most points are far away, and approximately the same distance”?
So I can't understand the statement can you show me how this proves “most points are far away, and approximately the same distance”
Thank you