15.1.22 Theory of random processes

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