How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$?
Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-dimensional cube , $x=(x(1),...x(d))$ the generic point has its -th component $x(i)$ chosen uniformly at random in$ [0,1] $independently of other components and points.
$\Theta(d)$ represent the largest possible distance is d.
I try to reconduct this problem to Bertrand Paradox but i dont think is right. Maybe I that show that $E(||x−y||2)=Θ(d)$ , because is a hint but i dont know how.
but is different to my point.