Given a discrete system, use the unilateral transform to solve for the following: $(20$ points$)$

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

a$.$ Transfer function $H(z)=\frac{Y(z)}{x(z)}$

b$.$ Given the input of $x[n]=u[n],$ solve for $y[n]$

c$.$ Find initial and final values of $y[0]$ and $y[]$ using the initial and final theorems.