Random Vector

Definition

$\mathbf{X}:(\Omega ,\mathcal{F})\to ({\mathbb{R}}^d,{\mathcal{R}}^d),\mathbf{X}=(X_1,X_2,\dots ,X_d)$

Column vector whose components are random variables $X:(\Omega ,\mathcal{F})\to (\mathbb{R},\mathcal{R})$.

$\mathbf{X}(\omega )=(X_1,X_2,\dots ,X_d)(\omega )=(X_1(\omega ),X_2(\omega ),\dots ,X_d(\omega ))=(x_1,x_2,\dots ,x_d)$