Please complete this problem in RStudio and submit a knitted PDF document created from an R Markdown

source.

$1$ ECDFs

Generate $100$ observations from a $N(0,1)$ distribution using the rnorm$()$ function. Repeat this process $1000$

times, and generate the y values of an ECDF for each, saving the results as a data.frame or matrix object $($so

each ECDF vector is a column or row in the storage object$).$

Compute the ECDFs at a resolution of $x=0\mathrm{.}01$ over the range xin$[-4,4]$; that is$,$ for

xin$\{-4\mathrm{.}00,-3\mathrm{.}99,-3\mathrm{.}98,$cdots,$3\mathrm{.}98,3\mathrm{.}99,4\mathrm{.}00\}.$

Once the ECDFs are computed, find the point$-$wise mean $(hat())$ and standard deviation $(hat())$ across the ECDFs by

$x$ value, i$.$e$.,$ work across the columns $($if the ECDFs are stored by row$)$ or rows $($if the ECDFs are stored by

column$)$ of the storage object.

Conclude by making a plot. On a single set of axes $($one plot!$),$ display $10$ randomly $($you should include the

code to randomly select the ten!$)$ selected ECDFs from the set of $1000.$ Display them using a light colour $($e$.$g$.,$

grey$85),$ then put the mean ECDF $($above$)$ hat$()$ overtop in black, along with two additional lines at hat$()+-2*hat()$ in

red. Label this plot neatly.