code class$=$"asciimath"$>$Consider the following time series: xt $=0\mathrm{.}2$xt$-1+0\mathrm{.}8$xt$-2+$wt $-1\mathrm{.}2$wt$-1+0\mathrm{.}2$wt$-2,$ wt is a white noise process with variance $\backslash$sigma $2.($a$)$ Write down the reduced form of this model if it can be simplified. $(5$ pts$)($b$)$ Is this model invertible and stationary? $(5$ pts$)($c$)$ If invertible, transform this model into MA$(\backslash$infty $)$ with the representation xt $=$ wt $+$P$\backslash$infty write the first four terms of $\backslash$pi j and the recursive formula for general $\backslash$pi j$.(10$ pts$)$