15.1.4 Theory of random processes

Problem: The random process \( X(t) \) is given by the canonical expansion \( \quad X(t)=(t+1) u+\sin t \cdot v+e^{-3 t} \), where \( D(u)=D(v)=3 \). Find: a) the characteristics of the random process \( X(t) \); b) the characteristics of the random process \[ Y(t)=e^{2 t} \int_{0}^{t} X(\tau) d \tau \text {. } \]