15.1.33 Theory of random processes

Problem: The random function \( X(t)=t+X_{1} \cos t+ \) \( +X_{2} \sin t \) is given, where the random vector \( \left(\mathrm{X}_{1}, \mathrm{X}_{2}\right) \) has the expected value \( (-1 / 2 ; 1) \) and the correlation matrix \( \left(\begin{array}{cc}3 & -2 \\ -2 & 2,9\end{array}\right) \). Construct a canonical expansion of the process, find its expected value, dispersion and correlation function: