# Consider the random process of Problem 6.3. a. Find the time-average mean and the autocorrelation…

Consider the random process of Problem 6.3.

a. Find the time-average mean and the autocorrelation function.

b. Find the ensemble-average mean and the autocorrelation function.

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Problem 6.3

A random process is composed of sample functions that are square waves, each with constant amplitude A, period T0, and random delay τ as sketched in Figure 6.15. The pdf of τ is

a. Sketch several typical sample functions.

b. Write the first-order pdf for this random process at some arbitrary time t0. (Hint: Because of the random delay τ, the pdf is independent of t0. Also, it might be easier to deduce the cdf and differentiate it to get the pdf.)