Submission Instruction $1.$

Print this document, write your answers on the printed stapled document, and submit.

Be clear, precise, and to the point. Illegible$/$unjustified answers will receive zero grade.

Question $1(20$ pts$)$

$($iii$)$ In R$,$ generate an univariate sample of size $n=100$ with rnorm$(n)$ and do the following

$($see code example screenshot below$)$:

$($a$)$ Compute $\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}){)}^2.$

$($b$)$ Compute $\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i^2-{\stackrel{}{x}}^2.$

$($c$)$ var$(x).$

Report your results. By $($i$),($a$)$ and $($b$)$ must be the same. Verify that $\frac{n}{n-1}($c$)$ is equal to

$($a$).$ Therefore, what is the formula being computed by the var$()$ function? $($This formula is

called the sample variance.$)$