Problem $5$

Consider a discrete$-$time linear time$-$invariant $($LTI$)$ system described by the following difference equation:

$y[n]-0\mathrm{.}5y[n-1]+0\mathrm{.}25y[n-2]=x[n]+0\mathrm{.}5x[n-1]$

Find the transfer function $H(z)$ of the system using the Z$-$transform.

Determine the poles and zeros of the system.

A system is called stable if all poles lie within the unit circle. Is this system stable?