\frac{1}{n} \sum_{i=1}^{n} \mathbf{X}_i= \frac{1}{n}\begin{bmatrix} \sum_{i=1}^{n} X_{i(1)} \\ \vdots \\ \sum_{i=1}^{n} X_{i(k)} \end{bmatrix} = \begin{bmatrix} \bar X_{i(1)} \\ \vdots \\ \bar X_{i(k)} \end{bmatrix}=\mathbf{\bar X_n} .
\frac{1}{\sqrt{n}} \sum_{i=1}^{n} \left [\mathbf{X}_i - \operatorname{E}\left ( X_i\right ) \right ]=\frac{1}{\sqrt{n}}\sum_{i=1}^{n} ( \mathbf{X}_i - \boldsymbol\mu ) = \sqrt{n}\left(\overline{\mathbf{X}}_n - \boldsymbol\mu\right) .