Sub-Gaussian random vector

Prove that any subvector of an isotropic Sub-Gaussian random vector is an isotropic Sub-Gaussian random vector.

Let $$X \in \mathbb{R}^{n}$$ be an isotropic Sub-Gaussian random vector. Then we know that $$EX=0$$, $$Cov(X)=I_n$$, and $$E[(X^Ta)^2)]=||a||^{2}_{2}$$ for all $$a\in \mathbb{R}^{n}$$. Also, for any $$a\in \mathbb{R}^{n}, a \ne 0, X^Ta$$ is a Sub-Gaussian random variable.

• And what have you tried? – Don Thousand Oct 15 '18 at 20:06