Consider the random process of Problem 7.3.
(a) Find the time-average mean and the auto correlation function.
(b) Find the ensemble-average mean and the auto correlation function.
(c) Is this process wide-sense stationary? Why or why not?

Data From Problem 7.3

A random process is composed of sample functions that are square waves, each with constant amplitude T₀, and random delay Ï„ as sketched in Figure 7.15. The pdf of Ï„ is 

Figure 7.15

(a) Sketch several typical sample functions.
(b) Write the first-order pdf for this random process at some arbitrary time t₀. (Because of the random delay Ï„, the pdf is independent of t₀. Also, it might be easier to deduce the cdf and differentiate it to get the pdf.)

S 1/T,, |7| < To/2 0, f (t) = otherwise X(t) - To