$($b$)$ Consider a causal LTI system described by the following LCCDE:

$y[n]+0\mathrm{.}2y[n-1]-0\mathrm{.}24y[n-2]=x[n]+x[n-1]$

i$)$ Obtain the system transfer function $H(z)$; $(3\text{'})$

ii$)$ Discuss the ROC and stability of the system; $(2\text{'})$

iii$)$ Find the system output to a unit step function $u[n].$