Consider signal detection principles for two overlapping internal probability distributions (over internal neural signals, denoted z), conditional on a signal s being present along with noise n (denoted s&n), or conditional on only noise being present (denoted n); where the corresponding internal probability distributions are denoted d(z| s&n ) and d(z| n ) respectively. What is the definition of the Likelihood Ratio function, and what is the optimal rule for responding to internal z-signals ? Draw a diagram of the two overlapping internal probability distributions, and show the two areas corresponding to the r and w signal detection probabilities. Use questions 1 and 2 to show theoretically how to move along an ROC curve, and how to shift the entire ROC to become more bowed or less bowed [corresponding to easier or harder detection respectively]