In signal detection, an observer is assigned the task of discerning the presence (or absence) of some signal with accompanying noise. There are four possible outcomes: a hit ($H$), a miss, a false alarm ($FA$), or a correct rejection. An iso-sensitivity function is the function that describes the relation between correct and false reports of a difference, with $P(H)$ on the $y$-axis and $P(FA)$ on the $x$-axis.
If $P(H) = p + (1-p)P(FA)$
and $P(FA) = g$ (guess)
and $p$, $g$ both lie between $0$ and $1$,
can someone walk me through how to derive the prediction for the iso-sensitivity function in ROC space? (Or point me to some source that can clearly explain this)?