End points of ROC, DET, PRC: For a binary classification task with a dataset of N negative samples and P positive samples, what are the coordinates of the two end points $($ordered by the X coordinates$)$ of the

following curves?

ROC $($y$=$ TPR vs$.$ x$=$FPR$)$

DET$($y$=$FNR vs$.$ x$=$FPR$)$

PRC $($ y$=$ precision vs$.$ x$=$ recall$),$ where the sample with the biggest likelihood is positive.

PRC $($ y$=$ precision vs$.$ x$=$ recall$),$ where the sample with the biggest likelihood is negative $($which is rare but it could happen$).$

$($Note that if an end point has $0//0($or NaN, not a number$)$ as its component, then it is not a legal end point since we cannot plot it$.$ In this case, you need to adopt the next$/$previous non$-$NaN end point.$)$

I already know the endpoints of ROC and DET, and I need to know the detailed explanations of the last two questions of PRC$.$ Thanks.