15.1.6 Theory of random processes

Problem: The random function \( X(t) \) has the characteristics \( m_{X}(t)=0, \quad k_{x}\left(t, t^{\prime}\right)=\frac{1}{1+\left(t-t^{\prime}\right)^{2}} \). Find the characteristics of the random function \( Y(t)=\int_{0}^{t} X(t) d t \) and find out whether \( X(t), Y(t) \) are stationary?