P$-7\mathrm{.}16$ Consider the signal x$[$n$]=$ u$[$n$]$u$[$n$5]$

$($a$)$ Determine Cxx$[$n$],$ the autocorrelation function $($acf$)$ of this signal.

$($b$)$ Determine the DTFT of the acf; verify that it is purely real and nonnegative.

$($c$)$ Determine the acf of the signal y$[$n$]=$ x$[$n $-2].$ Hints: Since the peak value of an acf must always be at zero lag, consider the possibility that cyy $[$n$]$ might be the same as Cxx$[$n$].$ Working with the DTFT of the acf might be easier.