Repeat the previous problem when two single delay line cancelers are cascaded to produce a double delay line canceler. Let \(X(t)\) be a stationary random process, \(E[X(t)]=1\), and the autocorrelation \(\mathfrak{R}_{x}(\tau)=3+\exp \{-|\tau|\}\). Define a new random variola \(Y\) as

\[
Y=\int_{0}^{2} x(t) d t
\]

Compute \(E[Y(t)]\) and \(\sigma_{Y}^{2}\).

Data From Previous Problem

Let the random variable \(Z\) be written in terms of two other random variables \(X\) and \(Y\) as follows: \(Z=X+3 Y\). Find the mean and variance for the new random variable in terms of the other two.