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

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

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

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

the are under the ROC curve$($AUC$)$ can be used as a measure of the classifiers performance