A modulated signal (pulse code modulation) {X(t), t ∈ (−∞, +∞)} is given by where the A n are independent and identically distributed random variables which can only take on values −1 and +1 and have...

A modulated signal (pulse code modulation) {X(t), t ∈ (−∞, +∞)} is given by

where the A_n
are independent and identically distributed random variables which can only take on values −1 and +1 and have mean value 0. Further, let

1) Sketch a section of a possible sample path of the process {X(t), t ∈ (−∞, +∞)}.

2) Determine the covariance function of this process.

3) Let Y(t) = X(t − Z), where the random variable Z has a uniform distribution over [0, 1]. Is the stochastic process {Y(t), t ∈ (−∞, +∞)} weakly stationary?