Consider that you have generated a classifier. The following table lists the $10$ test instances used for evaluating your model, where $\backslash (\backslash$mathrm$\{$P$\}(+)\backslash )$ in the $\backslash (2^\{\backslash$text $\{$nd $\}\}\backslash )$ column is the $"+"$ class membership probability that your model estimates for each instance.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline Instance Number & $\backslash (\backslash$mathrm$\{$P$\}(+)\backslash )$ & Actual Label $\backslash \backslash$

$\backslash$hline $1$ & $\mathrm{.}72$ & $-\backslash \backslash$

$\backslash$hline $2$ & $\mathrm{.}65$ & $+\backslash \backslash$

$\backslash$hline $3$ & $\mathrm{.}53$ & $+\backslash \backslash$

$\backslash$hline $4$ & $\mathrm{.}39$ & $-\backslash \backslash$

$\backslash$hline $5$ & $\mathrm{.}11$ & $-\backslash \backslash$

$\backslash$hline $6$ & $\mathrm{.}87$ & $+\backslash \backslash$

$\backslash$hline $7$ & $\mathrm{.}06$ & $-\backslash \backslash$

$\backslash$hline $8$ & $\mathrm{.}28$ & $+\backslash \backslash$

$\backslash$hline $9$ & $\mathrm{.}96$ & $+\backslash \backslash$

$\backslash$hline $10$ & $\mathrm{.}43$ & $-\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$1)$ Sort the list in descending order of the $"+"$ class membership probability. Show your sorted list in your report;

$2)$ Construct a ROC curve for this testing dataset. Show the coordinates $($i$.$e$.,$ the FPR and TPR$)$ of each point on your ROC curve;

$3)$ Calculate the AUC of the ROC curve. Show your calculation and result in your report.