$x[n]$ is a discrete$-$time zero mean wide sense stationary Gaussian process with autocorrelation

function $R_x(k)=2^{(2-|k|)}.$ Define the following process:

$Y[n]=\frac{1}{2}x[n-1]-\frac{1}{4}x[n-2]$

$($a$)$ Find Var$(x[n]).$

$-[x^2]$

$2-e^{-1}$

$($b$)$ Find $f_{x[n]}(x),$ the pdf of $x[n].$ Is it a function of time?

$($c$)$ Find $f_{x[n],x[n+1]}(x_0,x_1),$ the joint pdf of $x[n]$ and $x[n+1].$

$($d$)$ Find $E[Y[n]].$

$\underset{0}{lim}R*{*}^{(k)}$