Let \(t_{k}\) be the test outcome for the diseased \((k=1)\) and nondiseased \((k=0)\) subject. Show

(a) \(\mathrm{AUC}=\operatorname{Pr}\left(t_{1} \geq t_{0}\right)\) if \(t_{k}\) is continuous;

(b) \(\mathrm{AUC}=\operatorname{Pr}\left(t_{1}>t_{0}\right)+\frac{1}{2} \operatorname{Pr}\left(t_{1}=t_{0}\right)\) if \(t_{k}\) is discrete.