#kernel-algebra

Question 1: Single choice

$f \sim \mathcal{GP}(m_1, k_1)$ and $g \sim \mathcal{GP}(m_2, k_2)$ are independent, and $u(x) = f(x) + 2g(x)$ . What is $u$ ?

A GP with mean $m_1 + 2m_2$ and covariance $k_1 + 4k_2$ 1
A GP with mean $m_1 + 2m_2$ and covariance $k_1 + 2k_2$ 2
A GP with covariance $k_1 + 4k_2$ plus a cross-covariance term between $f$ and $g$ 3
Not a GP, since a sum of two random functions is not Gaussian in general4