ROC curves and AUC:

There are reference answers on-line here here, here and here.

DEFINITIONS:

\(\text{Sensitivity or TP Rate} = \frac{TP}{TP\, +\, FN}\)


\(\text{Specificity} = \frac{TN}{TN\, +\, FP}\)


\(\text{FP Rate or Fall-out} = \frac{FP}{TN\, +\, FP} = 1 - \text{Specificity}\)