A random process is defined as $x[n]=\frac{1}{2}(a[n]+a[n-1])$

where $a[n]$ is an i$.$i$.$d$.$ sequence of $U(-1,1)$ variables.

$($a$)$ Compute the mean and the variance of $x[n].$

$($b$)$ Specify the first$-$order PDF of $x[n].$

$($c$)$ Determine the autocorrelation function of $x[n].$