15.1.1 Theory of random processes

Problem: An elementary random function has the form \( Y(t)=a X+t \), where \( X \) is a random variable, distributed in accordance with the normal law with the parameters \( m, \sigma\left(p(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-m)^{2}}{2 \sigma^{2}}}\right) \), \( a \) is a non-random value. Find the characteristics of the elementary random function \( Y(t) \).