Problem$-2$: ROC Curve $[60$ points$]$

You are asked to evaluate the performance of two classification models, M$1$ and

M$2.$ The following table shows the probabilities obtained by applying the models

to the test set:

Plot the ROC curve for both $M1$ and $M2.$ Show all the intermediate calculations

as we discussed in the class. That includes calculations for TP$,$ FP$,$ TN$,$ FN$,$ TPR$,$

and FPR$.$ The use of a spreadsheet $($MS Excel$)$ is allowed but not R$/$Python$.$ You

should plot them on the same graph $[15$ points for M$1+15$ points for M$2].$

Which model do you think is better? Explain your reasons $[5$ points$].$