Consider the process:

$y_t=2+0\mathrm{.}5lo{n}_{t-1}+lo{n}_t$ with $lo{n}_{t}N(0,{}_t^2)$

${}_t^2=1+0\mathrm{.}3lo{n}_{t-1}^2+0\mathrm{.}2{}_{t-1}^2$

Find the unconditional variance of $y_t,$ i$.$e$.,$ Var$[y_t].$

$1$

$1\mathrm{.}25($This is not the answer$)$

$2\mathrm{.}5$

$2$