Consider the random process \(Z(t)=U \cos \pi t\), where \(U\) is a random variable with probability density function

\[ p_{U}(u)=\frac{1}{\sqrt{2 \pi}} \exp \left(-\frac{u^{2}}{2}\right) \]

(a) What is the probability density function of the random variable \(Z(0)\) ?

(b) What is the joint density function of \(Z(0)\) and \(Z(1)\) ?

(c) Is this random process strictly stationary, wide-sense stationary, or ergodic?