A certain random process (U(t)) consists of a sum of (possibly overlapping) pulses of the form (pleft(t-t_{k} ight)=operatorname{rect}left(left(t-t_{k} ight) / b ight)) occurring with mean

A certain random process \(U(t)\) consists of a sum of (possibly overlapping) pulses of the form \(p\left(t-t_{k}\right)=\operatorname{rect}\left(\left(t-t_{k}\right) / b\right)\) occurring with mean rate \(\bar{n}\) pulses per second. The times of occurrence are completely random, with the number of pulses being emitted in a \(T\)-second interval being Poisson distributed with mean \(\bar{n} T\). This random input is applied to a nonlinear device with input-output characteristic

\[ z= \begin{cases}1 & u>0 \\ 0 & u=0\end{cases} \]

Find \(\bar{z}\) and \(\Gamma_{Z}(\tau)\).