15.1.7 Theory of random processes

Problem: The random process has the form: \( X(t)=V \cdot e^{-t}+a t^{2} \), where \( V \) is a random value, distributed according to the exponential law with the parameter \( \lambda, a= \) const. Find the expected value, the mathematical expectation, the normalized autocovariance function and the dispersion of \( t^{2} X(t) \).