Question $4($Z$-$transform and LTID system$)$

$($a$)$ Consider the input and output pairs listed below. For each case, determine the system transfer function $H(z)$ along with its ROC, and indicate if the system considered is stable and$/$or causal.

i$),x[n]=(\frac{1}{2}{)}^{n}u[n],y[n]=3(\frac{1}{2}{)}^{n}u[n]+2(\frac{3}{4}{)}^{n}u[n]$;

ii$)x[n]=1\mathrm{.}25[n]-0\mathrm{.}25(0\mathrm{.}8{)}^{n}u[n],y[n]=(0\mathrm{.}8{)}^{n}u[n].$