ThmDex – An index of mathematical definitions, results, and conjectures.

Components of standard gaussian random euclidean real number are standard gaussian random basic real numbers

Formulation 0

Let $Z = (Z_1, \ldots, Z_D) \in \mathsf{MVGaussian}_D(0, I_D)$ be a D5273: Standard gaussian random euclidean real number.

Then \begin{equation} Z_1, \ldots, Z_D \overset{d}{=} \mathsf{Gaussian}(0, 1) \end{equation}

Proofs

Proof 0

Let $Z = (Z_1, \ldots, Z_D) \in \mathsf{MVGaussian}_D(0, I_D)$ be a D5273: Standard gaussian random euclidean real number.