# multivariate distribution with units

04 Nov 2020Imagine a set \(\left\{x_i\right\}\) of random numbers, all with different units, which follow a multivariate Gaussian distribution with the covariance \(C_{ij}=\langle x_i x_j\rangle\). Can you show that \(x_i(C^{-1})_{ij}x_j\) and \(\mathrm{d}^n x/\sqrt{\mathrm{det}C}\) are dimensionless?