In the R$-$code provided $($which is below$),$ do the following:

n$=30$

biased$\_$sample$\_$variances$=$rep$($NA$,100)$

unbiased$\_$estimate$=$rep$($NA$,100)$

for$($i in $1$:$100)\{$

x$=$rnorm$($n$,$sd$=$sqrt$(2))$

biased$\_$sample$\_$variances$[$i$]=$sum$(($x$-$mean$($x$))^2)/$n

unbiased$\_$estimate$[$i$]=$sum$(($x$-$mean$($x$))^2)/($n$-1)$

$\}$

a$)$ Provide an intuitive explanation for what the code is doing.

b$)$ Provide code to estimate the bias and the variance of the two estimates calculated. How close are these to what we would expect?