Components of Multivariate normal, and their distributions I have a random vector X ~ Normal(m, $\Sigma$). Now, according to wiki, any linear combination of components of this random vector is normal. 1) But are the components of random vector themselves always normal? (Is there a way to combine non-normal RVs to make MVN, so that random vector X will contain non-normal RVs?) 2) Does each component of random vector X follow its respective marginal distribution of Normal(m, $\Sigma$)? For example, component $X_1$ will be normal if we marginalize $X_2, X_3, $ etc. in the MVN pdf? 3) If we take 2 components of this random vector, lets call them ($X_1$, $X_2$), then their covariance will be the entry $\Sigma_{12} = \Sigma_{21}$?

1) Yes. Since any particular component is a linear combination. For example $$ X_2 = 0 * X_1 + 1 * X_2 + 0 * X_3 + \ldots + 0 * X_n $$

2) Yes. If you marginalize some components then you'll get a subvector living in a space isomorphic to subspace of a projection of your original vector. For example $$ (X_1, X_2) \text{ is isomorphic to } (X_1, X_2, 0, \ldots, 0) $$ It follows then that the MVN property still holds.

3) Yes. It is its definition.