uestion$1.$ Given the difference equation y$($n$)=$ x$($n$)-0\mathrm{.}5$y$($n$-1)$ a$.$ calculate the system response y$($n$)$ for n $=0,1,...,4$ with the input x$($n$)(0\mathrm{.}5)$ a$($n$)$ and initial condition y$(-1)=1$; b$.$ calculate the system response y$($n$)$ forn $=0,1,...,4$ with the input x$($n$)=(0\mathrm{.}5)"$u$($n$)$ and zero initial condition y$(-1)=0.$ Question$2.$ Given the difference equation, y$($n$)=$ x$($n$)-0\mathrm{.}5$y$($n$-1)$ a$.$ find H$($z$)$; b$.$ determine the impulse response y$($n$)$ if the input x$($n$)=$ o$($n$)$: c$.$ determine the step response y$($n$)$ if the input x$($n$)=$ un$).$ Question$3.$ A digital system is described by the following difference equation: y$($n$)=0\mathrm{.}25$x$($n $2)+0\mathrm{.}5$y$($n $1)-0\mathrm{.}2$y $($n $2)$ Find the transfer function H$(2),$ the denominator polynomial A$($z$),$ and the numerator poly$-$ nomial B$(2).$