Consider the process

$(1$ B$)(10\mathrm{.}2$B$)$Xt $=(10\mathrm{.}5$B$)$at$,$ at $$ N

$$

$0,$ $2$

a

$.$

$($a$)$ Determine the recursive expression that gives the l$$step ahead forcasts bXn $($l$),$ for l $3.$

$(8)$

$($b$)$ If an $=1,$ Xn $=4,$ Xn$1=3,$ $2$

a $=2,$ find:

$($i$)$ bXn $(2)$; $(3)$

$($ii$)$ the variance of the forecast in $($b$)($i$)$; and $(8)$

$($iii$)$ the $95\%$ forecast limits for the forecast in $($b$)($i$).$