Let (left{a_{1}, a_{2}, ldots, a_{n} ight}) be a sequence of real numbers, and (left{Phi_{1}, Phi_{2}, ldots, Phi_{n}

Let \(\left\{a_{1}, a_{2}, \ldots, a_{n}\right\}\) be a sequence of real numbers, and \(\left\{\Phi_{1}, \Phi_{2}, \ldots, \Phi_{n}\right\}\) be a sequence of independent random variables, uniformly distributed over \([0,2 \pi]\).

Determine covariance and correlation function of the process \(\{X(t), t \in(-\infty,+\infty)\}\) given by

\[X(t)=\sum_{i=1}^{n} a_{i} \sin \left(\omega t+\Phi_{i}\right)\]