Q58Section ST (Statistics (Q11–Q65))58 of 65

Deprojecting a bivariate normal component

Let $(X_1,X_2,X_3)$ have $N_3(\boldsymbol{\mu}, \Sigma)$ distribution with $\boldsymbol{\mu} = \begin{pmatrix} 2 \ -3 \ 1 \end{pmatrix}$ and $\Sigma = \begin{pmatrix} 25 & -2 & 4 \ -2 & 4 & 1 \ 4 & 1 & 9 \end{pmatrix}$ . For which of the following vectors $\mathbf{a}$ , $X_2$ and $X_2 - \mathbf{a}^T \begin{pmatrix} X_1 \ X_2 \end{pmatrix}$ are independent?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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