$($i$)$ Suppose you have a binary classification problem, where you have a set of predictions and corresponding true labels. You are interested in evaluating the performance of the classifier using ROC curves. You are given the following data in Table Q$4$b$.$

Table Q$4$b$.$ Binary Classifier statistics

$\backslash$table$[[$Sample$,$True Label,$\backslash$table$[[$Classifier$],[$Score$]]],[1,0,0\mathrm{.}3],[2,0,0\mathrm{.}4],[3,1,0\mathrm{.}5],[4,1,0\mathrm{.}6],[5,1,0\mathrm{.}8],[6,0,0\mathrm{.}9]]$

You are required to:

$($i$)$ Calculate the true positive rate $($TPR$)$ and false positive rate $($FPR$)$ for each possible threshold.

$[10$ points$]$

$($ii$)$ Plot the resulting ROC curve.

$[5$ points$]$

Hint: Order the samples in descending order according to the classifier score.