$(20)$ The autocorrelation function for a real$-$valued stable sequence is defined as

$c_{}[n]={\displaystyle \underset{k=-}{\overset{}{}}}x[k]x[n+k]$

$($a$)(10)$ Show that the z$-$transform of $c_{}[n]$ is $C_{}(z)=x(z)x(z^{-1}).$ Determine the region of convergence for $C_{}(z).$

$($Hint: assume $x(z)$ has ROC of $x[n]=a^{n}u[n]C_{}(z)c_{}[n]C_{}(z)r_R<mi>|</mi><mi>z</mi><mi>|</mi>$

the past answer was not clear and enough.. about ROC and sub question b