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.

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

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

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

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