$($a$)$ Given the following unilateral z$-$transforms, find the inverse z$-$transform of each function: $($i$)$ X$($z$)=0\mathrm{.}5$z$2($z$1)($z$0\mathrm{.}5)($ii$)$ X$($z$)=0\mathrm{.}5$z $($z$1)($z$0\mathrm{.}5)($iii$)$ X$($z$)=0\mathrm{.}5($z$1)($z$0\mathrm{.}5)($iv$)$ X$($z$)=$ z z$2$z$+1($b$)$ Evaluate each x$[$n$]$ in part $($a$)$ for the first three nonzero values. EECS $50,$ Fall $20242($c$)$ Verify the results in part $($c$)$ by expanding each X$($z$)$ in part $($a$)$ into a power series using long division. $($d$)$ Use the final$-$value property to evaluate x$[$$]$ for each function in part $($a$)$