The square wave x(t) of Figure P4.5, having constant amplitude A, period T0, and time shift td, represents the sample function of a stochastic process X(t). The time shift td is a random variable, described by the probability density function

a. Determine the probability density function of the random variable X(tk), obtained by sampling the stochastic process X(t) at time tk.

b. Determine the mean and autocorrelation function of X(t) using ensemble averaging.

c. Determine the mean and autocorrelation function of X(t) using time averaging.

d. Establish whether or not X(t) is weakly stationary. In what sense is it ergodic