15.1.32 Theory of random processes

Problem: The correlation function \( K_{X}(\tau) \) of the stationary random function \( X(t) \) is given: \( K_{X}(\tau)=\sigma^{2} e^{-\alpha^{2} \tau^{2}} \). Find the correlation function of the random function \( Y(t)=a X^{\prime}(t) \).