Let $x(t)$ be a Gaussian i$.$i$.$d$.$ process with $E[x(t)]=0$ and and $E[x(t{)}^2]=1.$

$($a$)(10$ pts$)$ What conditions would need to be satisfied for $x(t)$ to be Wide Sense Stationary? Are they satisfied?

$($b$)(10pts)x(t)$ is input to a linear time invariant filter $h(t).$ Prove or disprove that the output $Y(t)$ is Strict Sense Stationary.