Consider we draw N iid values $x_1, x_2,...,x_N$ from an uniform distribution on $[- \epsilon, \epsilon]$. Can we calculate the expected minimum of their absolute values: $$ \mathrm{E}(\mathrm{min}(|x_1|,|x_2|,...,|x_n|)) $$
If yes, can we even generalize this in higher diemensions, that is $x_1, x_2,...,x_N \in \mathbb{R}^K$ and $|\cdot|$ beeing any norm that works.