15.1.29 Theory of random processes

Problem: Let the random function \( X(t) \) have the characteristics \( \quad m_{x}(t)=1, K_{x}(t, s)=e^{-(t-s)^{2}} \). Find the characteristics of the random functions \[ \begin{array}{l} Y=1+t-x, Z=t^{2}+x^{\prime} \sin t, U=t+x^{\prime \prime}, \\ V=\int_{0}^{t}(1+t) X(t) d t . \end{array} \] Find out wheter the functions \( X, Y, Z, U, V \) are stationary.