15.1.18 Theory of random processes

Problem: The random function \( X(t) \) is given by the canonical expansion \( X(t)=U\left(t^{3}+e^{t}\right)+ \) \( +V \cos t+t^{3} \), where \( D_{U}=0,1, D_{V}=0,6 \). Find the characteristics \( m_{Y}(t), K_{Y}\left(t_{1}, t_{2}\right), D_{Y}(t) \), if \[ Y(t)=\int_{0}^{t} \tau^{3} \cdot X(\tau) d \tau+\sin t \cdot X(t)+t^{4}-2 \]