A logistic classifier was fitted to data, and six fresh observations were used to assess the performance of this classifier. Here are the fitted logistic probabilities and the observations $($Y values$).$

## Logistics predictions Fresh data values

## $[1,]0\mathrm{.}900$

## $[2,]0\mathrm{.}270$

## $[3,]0\mathrm{.}370$

## $[4,]0\mathrm{.}571$

## $[5,]0\mathrm{.}931$

## $[6,]0\mathrm{.}200$

A$)$ Compute the ROC curve for this classifier and report the coordinates of the curve. To this end, use thresholding to turn the predicted values into the $0/1$ classes and for each threshold, compute confusion matrices and the usual performance measures $($FPR$,$TPR$).$ The list of all these performance measures gives the coordinates of the curve.

B$)$ Compute the area under the curve and write it here AUC $=\_\_\_.$ Briefly comment on the performance of this classifier.