Consider the integral process \{Z(t) :t ≥ 0\} defined by
Z (t) = \int_{0}^{t}{X(s)ds} for \{X (t)\} being a mean-zero stationary stochastic process with autocorrelation function R_{XX} (\tau) =e^{ -\alpha \left|\tau\right|}, in which \alpha is a positive constant. Find the crosscorrelation function of \{X (t)\} and \{Z (t)\} and the autocorrelation function for \{Z (t)\}.