Suppose you have a binary classification problem where the positive class is rare $($important$)$ in the dataset. You have trained a classifier on this dataset and generated a ROC curve. Which of the following statements is$/$are true? Select ALL the correct statements.

The ROC curve plots the true positive rate $($sensitivity$)$ against the false positive rate $(1-$specificity$)$ for varying classification thresholds.

An optimal classifier has an ROC curve that hugs the top left corner of the plot.

The area under the ROC curve $($AUC$)$ can be used as a measure of the classifier's performance. $q,$

$q,$ An ROC curve with an AUC of $0\mathrm{.}5$ indicates a random classifier that performs no better than chance.