0
$\begingroup$

Given $v$ a random Gaussian distributed vector, is it possible to prove that $r = Rv$ is also Gaussian distributed? Any formula-link-information on how to start working on it is highly appreciated.

Thanks.

$\endgroup$
0
$\begingroup$

HINT: The sum of Gaussian variables/vectors (not necessarily independent) is indeed Gaussian.


Hence, for each component of vector $r$ we can write $$r_i = (Rv)_i = \sum_{j} R_{ij} v_j,$$ which is indeed Gaussian, given that $v_j$ is Gaussian.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.