  Let $X_0, \ldots, X_l$ be independent standard Gaussian vectors in
$\mathbb{R}^d$ such that $l \leqslant d$. We derive an explicit formula for the
distribution of the volume of weighted Gaussian simplex without the origin --
$l$-dimensional simplex $\mathrm{conv}(\sigma_0X_0, \ldots, \sigma_lX_l)$
($\sigma_0, \ldots, \sigma_l > 0$).
