(Solved): 1. Let \( \left\{X_{n}, n \in Z\right\} \) be a discrete-time random process, defined as \[ X_{n}=2 ...

1. Let \( \left\{X_{n}, n \in Z\right\} \) be a discrete-time random process, defined as \[ X_{n}=2 \cos \left(\frac{\pi n}{8}+\Phi\right), \] where \( \Phi \sim \) Uniform \( (0,2 \pi) \). a. Find the mean function, \( \mu_{X}(n) \). b. Find the correlation function \( R_{X}(5,7) \). c. Is \( X_{n} \) a WSS process? 2. Let \( X(t) \) be a WSS Gaussian random process with \( \mu_{\mathrm{X}}(\mathrm{t})=1 \) and \( \mathrm{R}_{\mathrm{X}}(\tau)=6+4 \operatorname{sinc}(\tau) \), where \( \operatorname{inc}(\tau)=\frac{\sin (\pi \tau)}{\pi \tau} \). (a) Find \( P(1