Consider the following MA$(3)$ process:

y $=$ u $+0\mathrm{.}5$ut$1+0\mathrm{.}5$ut$20\mathrm{.}5$ut$3,$

where ut is a noise process with a mean of zero and a variance of $\backslash$sigma $.$

$($a$)$ Calculate the mean and variance of yt $.$

$($b$)$ Compute the autocorrelation function $($ACF$)$ for the process $\{$yt $\}.$