Q$1.$ Let $Y=(x,Z),$ where $x,Z$ are i$.$i$.$d$.$ from $N(,1),$ but $Z$ is missing. Observed data MLE hat$()=x.$

$($a$)$ Show that the $Q$ function in the E$-$step is given by:

$({}^{(t)}|)=-\frac{1}{2}[(-x{)}^2+(-{}^{(t)}{)}^2].$

$($b$)$ Find the M$-$step Update $-$ what should happen as $t?$

$($c$)$ Use an AI$-$based tool to simulate the M$-$step update process as $t.$ Compare this with the theoretical expectations and discuss any insights or anomalies observed. I want a definate solution not guidlines