15.1.20 Theory of random processes

Problem: The random function \( X(t) \) is given by the canonical expansion \( X(t)=U \cdot e^{-t}+V \sin t+4 W \), where \( D_{U}=1, D_{V}=2, D_{W}=0,7 \). Find the characteristics of the random function \( Y(t): m_{Y}(t), K_{Y}\left(t_{1}, t_{2}\right), D_{Y}(t) \), where \[ Y(t)=2 X(t)+3 \int_{0}^{t} \tau X(\tau) d \tau \text {. } \]