$\{n_t\}$ is a gaussian Wide-Sense-Stationary process. $\mathbb{E}(n_t)=0, R_{n} (\tau) = N_0 \delta(\tau)$
$$X_t = \int_{0}^{2\pi} n(t) \cos(t) dt \quad Y_t = \int_{0}^{2\pi} n(t) \sin(t) dt$$ I found their expectation and variance to be finite values, and then I was asked whether they were gaussian and if they were whether or not they were dependent.
they’re gaussian because $n(t)\cos(t)$ is a gaussian process according to the solution (why?), and the solution then proves statistical independence ( I understand how). But how did they know to go for a proof in this case? what are the “flags” I should have noticed?